Prophet Model Overview and Performance
Prophet Configuration
Prophet Model Overview Facebook Prophet model for time series forecasting with seasonality and holiday effects
Model Overview
The Prophet model overview indicates that the growth type is linear, seasonality mode is additive, and there are 25 changepoints detected. Here’s how these settings impact the forecast:
Growth Type (Linear vs. Logistic):
Seasonality Mode (Additive vs. Multiplicative):
Changepoints:
In summary, using a linear growth type will lead to a forecast with a constant rate of change, additive seasonality will account for consistent seasonal patterns, and detecting 25 changepoints will help capture major shifts in the trend. These settings collectively aim to provide a robust forecast that incorporates both trend, seasonality, and abrupt changes in the time series data.
Model Overview
The Prophet model overview indicates that the growth type is linear, seasonality mode is additive, and there are 25 changepoints detected. Here’s how these settings impact the forecast:
Growth Type (Linear vs. Logistic):
Seasonality Mode (Additive vs. Multiplicative):
Changepoints:
In summary, using a linear growth type will lead to a forecast with a constant rate of change, additive seasonality will account for consistent seasonal patterns, and detecting 25 changepoints will help capture major shifts in the trend. These settings collectively aim to provide a robust forecast that incorporates both trend, seasonality, and abrupt changes in the time series data.
Accuracy Metrics
Forecast Performance Metrics Model accuracy and prediction performance indicators
Forecast Performance
MAE (Mean Absolute Error) measures the average magnitude of errors without considering their direction. In this case, the MAE of 4.1561 suggests, on average, the forecast error is approximately 4.16 units.
RMSE (Root Mean Squared Error) provides a more comprehensive understanding of the forecast errors by penalizing larger errors more heavily. A RMSE value of 5.1671 indicates the model’s forecast errors have greater variability compared to MAE, with an average deviation of 5.17 units.
MAPE (Mean Absolute Percentage Error) is the percentage of the absolute errors relative to the actual values. An MAPE of 3.43% signifies the average percentage error in the forecasts is around 3.43%.
Coverage represents the proportion of actual values falling within the forecast prediction intervals. For this data, a coverage of 95.4% indicates that about 95.4% of the actual values are within the forecasted range.
In terms of forecast reliability, the lower the MAE, RMSE, and MAPE values, the more accurate the forecasts are. A high coverage percentage suggests the model’s prediction intervals capture the actual values well.
Whether these error rates are acceptable for business planning depends on the specific context and industry. Lower error rates are generally preferred, especially in industries where precision is critical, such as finance or healthcare. A coverage of 95.4% is quite high and indicates a good level of forecast reliability. However, it is advisable to compare these metrics with industry standards or previous performance to determine if further refinement of the forecasting model is needed.
Forecast Performance
MAE (Mean Absolute Error) measures the average magnitude of errors without considering their direction. In this case, the MAE of 4.1561 suggests, on average, the forecast error is approximately 4.16 units.
RMSE (Root Mean Squared Error) provides a more comprehensive understanding of the forecast errors by penalizing larger errors more heavily. A RMSE value of 5.1671 indicates the model’s forecast errors have greater variability compared to MAE, with an average deviation of 5.17 units.
MAPE (Mean Absolute Percentage Error) is the percentage of the absolute errors relative to the actual values. An MAPE of 3.43% signifies the average percentage error in the forecasts is around 3.43%.
Coverage represents the proportion of actual values falling within the forecast prediction intervals. For this data, a coverage of 95.4% indicates that about 95.4% of the actual values are within the forecasted range.
In terms of forecast reliability, the lower the MAE, RMSE, and MAPE values, the more accurate the forecasts are. A high coverage percentage suggests the model’s prediction intervals capture the actual values well.
Whether these error rates are acceptable for business planning depends on the specific context and industry. Lower error rates are generally preferred, especially in industries where precision is critical, such as finance or healthcare. A coverage of 95.4% is quite high and indicates a good level of forecast reliability. However, it is advisable to compare these metrics with industry standards or previous performance to determine if further refinement of the forecasting model is needed.
Historical Data and Future Predictions
Historical and Predicted Values
Time Series Forecast — Historical data with future predictions and confidence intervals
Time Series Forecast
Based on the data profile provided, we are working with a time series forecast that includes historical data, future predictions, and confidence intervals.
Analyzing the historical patterns is essential to understand how the forecast extends from them. It is crucial to identify any trends, seasonality, or anomalies present in the historical data. These patterns serve as the basis for generating accurate forecasts.
The confidence intervals are significant as they provide a range within which the actual values are likely to fall. The width of the confidence intervals over the forecast horizon can vary based on the model’s complexity and the level of uncertainty in the data. A wider confidence interval indicates higher uncertainty in the predictions.
When examining the historical data, any interesting patterns or anomalies should be noted. These anomalies could include sudden spikes or drops in the data that may impact the accuracy of the forecast. Understanding these anomalies is crucial for adjusting the model or taking them into account when making future predictions.
Overall, by examining the historical patterns, understanding the width of the confidence intervals, and noting any anomalies, we can gain valuable insights into the time series forecast and make informed decisions based on the predicted future values.
Time Series Forecast
Based on the data profile provided, we are working with a time series forecast that includes historical data, future predictions, and confidence intervals.
Analyzing the historical patterns is essential to understand how the forecast extends from them. It is crucial to identify any trends, seasonality, or anomalies present in the historical data. These patterns serve as the basis for generating accurate forecasts.
The confidence intervals are significant as they provide a range within which the actual values are likely to fall. The width of the confidence intervals over the forecast horizon can vary based on the model’s complexity and the level of uncertainty in the data. A wider confidence interval indicates higher uncertainty in the predictions.
When examining the historical data, any interesting patterns or anomalies should be noted. These anomalies could include sudden spikes or drops in the data that may impact the accuracy of the forecast. Understanding these anomalies is crucial for adjusting the model or taking them into account when making future predictions.
Overall, by examining the historical patterns, understanding the width of the confidence intervals, and noting any anomalies, we can gain valuable insights into the time series forecast and make informed decisions based on the predicted future values.
Long-term Trend and Changepoints
Long-term Trend Analysis
Trend Component — Long-term trend with changepoints marked
Trend Component
Based on the description provided, the long-term trend component shows the overall direction of the data with specific time points marked as changepoints.
To provide more detailed insights or forecast future trends accurately, it would be beneficial to have access to the specific data points or information related to the long-term trend and changepoints. This would enable a more in-depth analysis of the trend components and their implications.
Trend Component
Based on the description provided, the long-term trend component shows the overall direction of the data with specific time points marked as changepoints.
To provide more detailed insights or forecast future trends accurately, it would be beneficial to have access to the specific data points or information related to the long-term trend and changepoints. This would enable a more in-depth analysis of the trend components and their implications.
Trend Change Dates
Changepoints Analysis Detected trend changepoints in the time series
| Changepoint | Index |
|---|---|
| 2021-02-02 | 1.000 |
| 2021-03-06 | 2.000 |
| 2021-04-07 | 3.000 |
| 2021-05-09 | 4.000 |
| 2021-06-11 | 5.000 |
| 2021-07-13 | 6.000 |
| 2021-08-14 | 7.000 |
| 2021-09-15 | 8.000 |
| 2021-10-17 | 9.000 |
| 2021-11-18 | 10.000 |
| 2021-12-20 | 11.000 |
| 2022-01-21 | 12.000 |
| 2022-02-23 | 13.000 |
| 2022-03-27 | 14.000 |
| 2022-04-28 | 15.000 |
| 2022-05-30 | 16.000 |
| 2022-07-01 | 17.000 |
| 2022-08-02 | 18.000 |
| 2022-09-03 | 19.000 |
| 2022-10-05 | 20.000 |
Changepoints
Based on the provided data profile, a changepoint analysis detected 25 trend changepoints in the time series. Changepoints represent points in time where a significant change or shift in the underlying trend of the time series data occurs. These changes can indicate shifts in patterns, behaviors, or factors influencing the data.
In this analysis, with 25 detected changepoints, it suggests that there are multiple instances where the trend experienced notable shifts. Major trend changes can help identify significant events or transitions that impacted the data. By analyzing when these changepoints occurred, one can potentially link them to external factors such as changes in regulations, economic conditions, technological advancements, or other events that could have influenced the time series data.
The changepoint prior scale of 0.05 indicates the flexibility in detecting changepoints. A lower changepoint prior scale leads to a more flexible model that can adapt to smaller changes in trend, potentially capturing more nuanced shifts in the data. However, this may also increase the likelihood of false positives or detecting noise as changepoints. On the other hand, a higher changepoint prior scale imposes a stricter criterion for detecting changepoints, potentially missing smaller but still relevant changes in the trend.
In conclusion, the changepoints identified in the time series data can provide valuable insights into the dynamics of the underlying trends and potential factors driving these changes. Understanding the timing of major trend changes and adjusting the changepoint prior scale can help in interpreting the analysis results effectively.
Changepoints
Based on the provided data profile, a changepoint analysis detected 25 trend changepoints in the time series. Changepoints represent points in time where a significant change or shift in the underlying trend of the time series data occurs. These changes can indicate shifts in patterns, behaviors, or factors influencing the data.
In this analysis, with 25 detected changepoints, it suggests that there are multiple instances where the trend experienced notable shifts. Major trend changes can help identify significant events or transitions that impacted the data. By analyzing when these changepoints occurred, one can potentially link them to external factors such as changes in regulations, economic conditions, technological advancements, or other events that could have influenced the time series data.
The changepoint prior scale of 0.05 indicates the flexibility in detecting changepoints. A lower changepoint prior scale leads to a more flexible model that can adapt to smaller changes in trend, potentially capturing more nuanced shifts in the data. However, this may also increase the likelihood of false positives or detecting noise as changepoints. On the other hand, a higher changepoint prior scale imposes a stricter criterion for detecting changepoints, potentially missing smaller but still relevant changes in the trend.
In conclusion, the changepoints identified in the time series data can provide valuable insights into the dynamics of the underlying trends and potential factors driving these changes. Understanding the timing of major trend changes and adjusting the changepoint prior scale can help in interpreting the analysis results effectively.
Annual Seasonal Patterns
Annual Seasonal Effects by Month
Yearly Seasonality Pattern — Annual seasonal effects by month
Yearly Seasonality
The yearly seasonality pattern shows that there are significant fluctuations in performance throughout the year, with a peak month in April and a trough month in October. The seasonal range, which represents the magnitude of these fluctuations, is 19.28 units.
April appears to be the peak month with the highest performance levels, while October marks the trough with the lowest performance levels. This information is valuable for business planning because it provides insight into when to expect peak demand or activity (April) as well as when to anticipate slower periods (October).
Understanding these monthly seasonal effects and their magnitudes can help in optimizing resource allocation. For instance, during the peak month of April, businesses may need to ramp up production, marketing efforts, and staffing to meet the increased demand. In contrast, during the trough month of October, they may consider cost-saving measures or focus on strategic planning rather than heavy operations.
For annual forecasting, this data suggests that overall performance is subject to seasonal variations that need to be accounted for in projections. By factoring in the peak and trough months, businesses can more accurately predict their yearly performance and adjust strategies accordingly.
In terms of resource allocation, businesses can use this information to streamline operations, adjust inventory levels, schedule promotions or sales to align with peak months, and ensure they have the necessary resources in place to meet varying demand throughout the year.
Yearly Seasonality
The yearly seasonality pattern shows that there are significant fluctuations in performance throughout the year, with a peak month in April and a trough month in October. The seasonal range, which represents the magnitude of these fluctuations, is 19.28 units.
April appears to be the peak month with the highest performance levels, while October marks the trough with the lowest performance levels. This information is valuable for business planning because it provides insight into when to expect peak demand or activity (April) as well as when to anticipate slower periods (October).
Understanding these monthly seasonal effects and their magnitudes can help in optimizing resource allocation. For instance, during the peak month of April, businesses may need to ramp up production, marketing efforts, and staffing to meet the increased demand. In contrast, during the trough month of October, they may consider cost-saving measures or focus on strategic planning rather than heavy operations.
For annual forecasting, this data suggests that overall performance is subject to seasonal variations that need to be accounted for in projections. By factoring in the peak and trough months, businesses can more accurately predict their yearly performance and adjust strategies accordingly.
In terms of resource allocation, businesses can use this information to streamline operations, adjust inventory levels, schedule promotions or sales to align with peak months, and ensure they have the necessary resources in place to meet varying demand throughout the year.
Day-of-Week Effects
Day-of-Week Effects
Weekly Seasonality Pattern — Day-of-week effects
Weekly Seasonality
Based on the provided data, we have insights into the day-of-week effects and weekend patterns. Here are the key findings:
These numbers represent the effects or impact on the given metric (such as sales, customer visits, etc.) on each specific day of the week compared to the average. Days like Saturday and Friday show positive effects, indicating higher performance, while days like Tuesday and Monday have negative effects.
Strongest and Weakest Days:
Weekend Effect:
Recommendations:
Understanding these day-of-week effects can help in optimizing operations, scheduling, and resource allocation to better align with the weekly seasonality patterns and maximize overall performance.
Weekly Seasonality
Based on the provided data, we have insights into the day-of-week effects and weekend patterns. Here are the key findings:
These numbers represent the effects or impact on the given metric (such as sales, customer visits, etc.) on each specific day of the week compared to the average. Days like Saturday and Friday show positive effects, indicating higher performance, while days like Tuesday and Monday have negative effects.
Strongest and Weakest Days:
Weekend Effect:
Recommendations:
Understanding these day-of-week effects can help in optimizing operations, scheduling, and resource allocation to better align with the weekly seasonality patterns and maximize overall performance.
Impact Analysis
Holiday Effects Impact of holidays on the time series
| Holiday | Effect |
|---|---|
| new_year | 28.900 |
| independence_day | 10.010 |
| thanksgiving | 15.340 |
| christmas | 21.870 |
Holiday Effects
Based on the given data profile, we have information about holiday effects on a time series dataset. Here are the insights derived from the data:
Impact Magnitude of Holidays:
Strongest Holiday Effects:
Holiday-Period Planning Recommendations:
In summary, understanding the impact of holidays on the time series data can help in making informed decisions related to resource allocation, marketing strategies, and inventory management during holiday periods. Prioritizing planning around high-impact holidays like New Year and Christmas can lead to better utilization of resources and maximized sales opportunities.
Holiday Effects
Based on the given data profile, we have information about holiday effects on a time series dataset. Here are the insights derived from the data:
Impact Magnitude of Holidays:
Strongest Holiday Effects:
Holiday-Period Planning Recommendations:
In summary, understanding the impact of holidays on the time series data can help in making informed decisions related to resource allocation, marketing strategies, and inventory management during holiday periods. Prioritizing planning around high-impact holidays like New Year and Christmas can lead to better utilization of resources and maximized sales opportunities.
Intraday Patterns
Hourly Effects (if enabled)
Daily Seasonality — Daily seasonality not enabled for this model
Daily Seasonality
The provided data indicates that daily seasonality was not enabled for the model, hence no hourly patterns were analyzed. The decision to not enable daily seasonality could stem from various reasons such as the data not exhibiting significant daily patterns or the analysis focusing on broader time trends rather than daily fluctuations.
Without the hourly patterns, we cannot identify peak and off-peak hours. However, it is important to understand that the absence of daily seasonality does not necessarily imply that the data lacks time-based patterns entirely. Other forms of seasonality or trends might still be present but operate on a longer time scale than daily periods.
To better understand the data and its patterns, it may be beneficial to examine higher-level trends or explore other time scales (e.g., weekly, monthly) to uncover insights that may not be apparent at a daily level.
Daily Seasonality
The provided data indicates that daily seasonality was not enabled for the model, hence no hourly patterns were analyzed. The decision to not enable daily seasonality could stem from various reasons such as the data not exhibiting significant daily patterns or the analysis focusing on broader time trends rather than daily fluctuations.
Without the hourly patterns, we cannot identify peak and off-peak hours. However, it is important to understand that the absence of daily seasonality does not necessarily imply that the data lacks time-based patterns entirely. Other forms of seasonality or trends might still be present but operate on a longer time scale than daily periods.
To better understand the data and its patterns, it may be beneficial to examine higher-level trends or explore other time scales (e.g., weekly, monthly) to uncover insights that may not be apparent at a daily level.
All Decomposed Components
All Components Combined
Complete Decomposition — All components: trend, yearly, weekly, and holiday effects
Full Decomposition
The data profile provided indicates that there is a complete decomposition of a dataset into trend, yearly, weekly, and holiday components. Each of these components plays a crucial role in understanding the underlying patterns and variations in the data.
Trend Component: The trend component captures the long-term direction in the data. It shows how the data is changing over time, irrespective of seasonality or other short-term fluctuations. Analyzing the trend component helps in identifying overall growth or decline patterns in the dataset.
Yearly Component: The yearly component represents the seasonality in the data that occurs on a yearly basis. This component captures periodic patterns that repeat every year, such as variations due to seasons or annual events. Understanding the yearly component is essential for identifying and planning for seasonal trends in the data.
Weekly Component: The weekly component captures the recurring patterns that happen on a weekly basis. It helps in understanding the fluctuations that occur within a week, which can be particularly important for businesses with weekly cycles or sales patterns. Analyzing the weekly component aids in identifying specific days of the week that show consistent high or low values.
Holiday Component: The holiday component reflects the impact of holidays or special events on the data. This component helps in understanding how holidays affect the overall trends and patterns in the dataset. Businesses can leverage this information to adjust their strategies and operations during holiday periods.
Relative Importance of Components:
Overall Decomposition and Business Implications: By decomposing the data into these components, businesses can gain a comprehensive understanding of the underlying patterns and factors affecting their dataset. This breakdown enables better forecasting, trend analysis, and decision-making. Understanding how trend, yearly, weekly, and holiday components combine allows businesses to tailor their strategies, promotional activities, inventory management, and resource allocation to maximize opportunities and mitigate risks associated with different temporal effects.
Full Decomposition
The data profile provided indicates that there is a complete decomposition of a dataset into trend, yearly, weekly, and holiday components. Each of these components plays a crucial role in understanding the underlying patterns and variations in the data.
Trend Component: The trend component captures the long-term direction in the data. It shows how the data is changing over time, irrespective of seasonality or other short-term fluctuations. Analyzing the trend component helps in identifying overall growth or decline patterns in the dataset.
Yearly Component: The yearly component represents the seasonality in the data that occurs on a yearly basis. This component captures periodic patterns that repeat every year, such as variations due to seasons or annual events. Understanding the yearly component is essential for identifying and planning for seasonal trends in the data.
Weekly Component: The weekly component captures the recurring patterns that happen on a weekly basis. It helps in understanding the fluctuations that occur within a week, which can be particularly important for businesses with weekly cycles or sales patterns. Analyzing the weekly component aids in identifying specific days of the week that show consistent high or low values.
Holiday Component: The holiday component reflects the impact of holidays or special events on the data. This component helps in understanding how holidays affect the overall trends and patterns in the dataset. Businesses can leverage this information to adjust their strategies and operations during holiday periods.
Relative Importance of Components:
Overall Decomposition and Business Implications: By decomposing the data into these components, businesses can gain a comprehensive understanding of the underlying patterns and factors affecting their dataset. This breakdown enables better forecasting, trend analysis, and decision-making. Understanding how trend, yearly, weekly, and holiday components combine allows businesses to tailor their strategies, promotional activities, inventory management, and resource allocation to maximize opportunities and mitigate risks associated with different temporal effects.
Residual Analysis and Fit Assessment
Model Diagnostics
Residual Analysis — Model residuals and diagnostic plots
Residual Analysis
The mean of the residuals is very close to zero (-0.0002), which is a positive sign indicating that the model is unbiased. The standard deviation of the residuals is 5.1697, which gives an indication of the spread of the residuals around the mean prediction.
Given that a normality test was conducted and passed (normality_test = true), it suggests that the residuals are likely normally distributed. This is an important assumption for many statistical models, and the fact that the residuals conform to this assumption is a good sign.
To check for patterns indicating model inadequacy, you could create diagnostic plots such as residuals vs. fitted values, residuals vs. time (if time series data), QQ plots, and autocorrelation plots. These plots can help identify patterns such as non-linearity, heteroscedasticity, autocorrelation, or outliers in the residuals, which would suggest issues with the model.
To assess whether the residuals appear to be white noise, you can look at the residual plots for randomness. White noise residuals should exhibit no discernible patterns, and any deviations from randomness could indicate that the model is not capturing all the underlying patterns in the data.
Overall, the mean and normality of the residuals, along with diagnostic plots, play a crucial role in evaluating the goodness-of-fit and assumptions of the model. It’s important to continue with further diagnostics to ensure the model adequacy and make any necessary adjustments if required.
Residual Analysis
The mean of the residuals is very close to zero (-0.0002), which is a positive sign indicating that the model is unbiased. The standard deviation of the residuals is 5.1697, which gives an indication of the spread of the residuals around the mean prediction.
Given that a normality test was conducted and passed (normality_test = true), it suggests that the residuals are likely normally distributed. This is an important assumption for many statistical models, and the fact that the residuals conform to this assumption is a good sign.
To check for patterns indicating model inadequacy, you could create diagnostic plots such as residuals vs. fitted values, residuals vs. time (if time series data), QQ plots, and autocorrelation plots. These plots can help identify patterns such as non-linearity, heteroscedasticity, autocorrelation, or outliers in the residuals, which would suggest issues with the model.
To assess whether the residuals appear to be white noise, you can look at the residual plots for randomness. White noise residuals should exhibit no discernible patterns, and any deviations from randomness could indicate that the model is not capturing all the underlying patterns in the data.
Overall, the mean and normality of the residuals, along with diagnostic plots, play a crucial role in evaluating the goodness-of-fit and assumptions of the model. It’s important to continue with further diagnostics to ensure the model adequacy and make any necessary adjustments if required.
Model Accuracy
Actual vs Predicted — Comparison of actual values against model predictions
Actual vs Predicted
The correlation value of 0.9661 indicates a strong positive linear relationship between the actual values and the model predictions. This suggests that the model does a good job at capturing the general trend in the data.
The R-squared value of 0.9333 indicates that approximately 93.33% of the variability in the actual values can be explained by the model. This indicates that the model is quite effective in predicting the outcomes based on historical data.
Given the high correlation and R-squared values, the model seems to be performing well in capturing historical patterns and making accurate predictions. The periods where the model performs well would be when the actual values closely align with the predicted values, indicating accurate forecasting. On the other hand, periods where the model performs poorly would be when there are significant deviations between the actual and predicted values, suggesting potential areas for improvement in the model.
Overall, with such high correlation and R-squared values, it appears that the model is reliable and effective in capturing historical patterns and predicting outcomes accurately.
Actual vs Predicted
The correlation value of 0.9661 indicates a strong positive linear relationship between the actual values and the model predictions. This suggests that the model does a good job at capturing the general trend in the data.
The R-squared value of 0.9333 indicates that approximately 93.33% of the variability in the actual values can be explained by the model. This indicates that the model is quite effective in predicting the outcomes based on historical data.
Given the high correlation and R-squared values, the model seems to be performing well in capturing historical patterns and making accurate predictions. The periods where the model performs well would be when the actual values closely align with the predicted values, indicating accurate forecasting. On the other hand, periods where the model performs poorly would be when there are significant deviations between the actual and predicted values, suggesting potential areas for improvement in the model.
Overall, with such high correlation and R-squared values, it appears that the model is reliable and effective in capturing historical patterns and predicting outcomes accurately.
Q-Q Plot
Normality Check — Q-Q plot for residual normality assessment
Normality Check
The Q-Q plot is a graphical tool used to assess whether a set of data follows a certain distribution, in this case, whether the residuals of a regression model are normally distributed. In the context of residual normality assessment, a Q-Q plot compares the quantiles of the residuals against the quantiles of a theoretical normal distribution.
Interpretation of the Q-Q plot for residual normality assessment:
Implications of non-normality for prediction intervals:
Whether transformations might improve the model:
In summary, assessing residual normality through a Q-Q plot is crucial for validating regression models. Deviations from normality can impact the quality of prediction intervals. Transformations can be a useful technique to address non-normality and potentially improve the model’s performance.
Normality Check
The Q-Q plot is a graphical tool used to assess whether a set of data follows a certain distribution, in this case, whether the residuals of a regression model are normally distributed. In the context of residual normality assessment, a Q-Q plot compares the quantiles of the residuals against the quantiles of a theoretical normal distribution.
Interpretation of the Q-Q plot for residual normality assessment:
Implications of non-normality for prediction intervals:
Whether transformations might improve the model:
In summary, assessing residual normality through a Q-Q plot is crucial for validating regression models. Deviations from normality can impact the quality of prediction intervals. Transformations can be a useful technique to address non-normality and potentially improve the model’s performance.
Model Validation
Model Accuracy
Actual vs Predicted — Comparison of actual values against model predictions
Actual vs Predicted
The correlation value of 0.9661 indicates a strong positive linear relationship between the actual values and the model predictions. This suggests that the model does a good job at capturing the general trend in the data.
The R-squared value of 0.9333 indicates that approximately 93.33% of the variability in the actual values can be explained by the model. This indicates that the model is quite effective in predicting the outcomes based on historical data.
Given the high correlation and R-squared values, the model seems to be performing well in capturing historical patterns and making accurate predictions. The periods where the model performs well would be when the actual values closely align with the predicted values, indicating accurate forecasting. On the other hand, periods where the model performs poorly would be when there are significant deviations between the actual and predicted values, suggesting potential areas for improvement in the model.
Overall, with such high correlation and R-squared values, it appears that the model is reliable and effective in capturing historical patterns and predicting outcomes accurately.
Actual vs Predicted
The correlation value of 0.9661 indicates a strong positive linear relationship between the actual values and the model predictions. This suggests that the model does a good job at capturing the general trend in the data.
The R-squared value of 0.9333 indicates that approximately 93.33% of the variability in the actual values can be explained by the model. This indicates that the model is quite effective in predicting the outcomes based on historical data.
Given the high correlation and R-squared values, the model seems to be performing well in capturing historical patterns and making accurate predictions. The periods where the model performs well would be when the actual values closely align with the predicted values, indicating accurate forecasting. On the other hand, periods where the model performs poorly would be when there are significant deviations between the actual and predicted values, suggesting potential areas for improvement in the model.
Overall, with such high correlation and R-squared values, it appears that the model is reliable and effective in capturing historical patterns and predicting outcomes accurately.
Q-Q Plot
Normality Check — Q-Q plot for residual normality assessment
Normality Check
The Q-Q plot is a graphical tool used to assess whether a set of data follows a certain distribution, in this case, whether the residuals of a regression model are normally distributed. In the context of residual normality assessment, a Q-Q plot compares the quantiles of the residuals against the quantiles of a theoretical normal distribution.
Interpretation of the Q-Q plot for residual normality assessment:
Implications of non-normality for prediction intervals:
Whether transformations might improve the model:
In summary, assessing residual normality through a Q-Q plot is crucial for validating regression models. Deviations from normality can impact the quality of prediction intervals. Transformations can be a useful technique to address non-normality and potentially improve the model’s performance.
Normality Check
The Q-Q plot is a graphical tool used to assess whether a set of data follows a certain distribution, in this case, whether the residuals of a regression model are normally distributed. In the context of residual normality assessment, a Q-Q plot compares the quantiles of the residuals against the quantiles of a theoretical normal distribution.
Interpretation of the Q-Q plot for residual normality assessment:
Implications of non-normality for prediction intervals:
Whether transformations might improve the model:
In summary, assessing residual normality through a Q-Q plot is crucial for validating regression models. Deviations from normality can impact the quality of prediction intervals. Transformations can be a useful technique to address non-normality and potentially improve the model’s performance.
Configuration and Forecasts
Prophet Parameters
Model Configuration Prophet model parameters and settings
| Parameter | Value |
|---|---|
| Growth Type | linear |
| Changepoint Prior Scale | 0.05 |
| Seasonality Prior Scale | 10 |
| Holidays Prior Scale | 10 |
| Seasonality Mode | additive |
| Number of Changepoints | 25 |
Model Configuration
The prior scales chosen for the Prophet model configuration play a critical role in determining the influence of various components like seasonality, growth, and holidays on the forecasting performance. Here’s a breakdown based on the provided information:
Changepoint Prior Scale (0.05):
Seasonality Prior Scale (10):
Holidays Prior Scale (10):
Seasonality Mode (additive):
Growth Type (linear):
Insights and Parameter Tuning Opportunities:
These insights and tuning opportunities could help enhance the forecasting accuracy and align the model more closely with the underlying data patterns.
Model Configuration
The prior scales chosen for the Prophet model configuration play a critical role in determining the influence of various components like seasonality, growth, and holidays on the forecasting performance. Here’s a breakdown based on the provided information:
Changepoint Prior Scale (0.05):
Seasonality Prior Scale (10):
Holidays Prior Scale (10):
Seasonality Mode (additive):
Growth Type (linear):
Insights and Parameter Tuning Opportunities:
These insights and tuning opportunities could help enhance the forecasting accuracy and align the model more closely with the underlying data patterns.
Detailed Predictions
Forecast Values Detailed forecast predictions with confidence intervals
| Date | Forecast | Lower_CI | Upper_CI |
|---|---|---|---|
| 2023-10-03 | 112.490 | 102.580 | 122.860 |
| 2023-10-04 | 115.120 | 104.990 | 125.250 |
| 2023-10-05 | 122.640 | 112.770 | 133.220 |
| 2023-10-06 | 130.500 | 120.280 | 139.750 |
| 2023-10-07 | 137.040 | 127.290 | 147.200 |
| 2023-10-08 | 132.240 | 122.750 | 142.360 |
| 2023-10-09 | 118.350 | 108.180 | 128.730 |
| 2023-10-10 | 112.830 | 102.840 | 123.410 |
| 2023-10-11 | 115.540 | 105.550 | 126.000 |
| 2023-10-12 | 123.170 | 112.940 | 133.120 |
| 2023-10-13 | 131.120 | 119.980 | 140.180 |
| 2023-10-14 | 137.760 | 127.990 | 147.680 |
| 2023-10-15 | 133.080 | 123.020 | 143.100 |
| 2023-10-16 | 119.300 | 108.760 | 129.350 |
| 2023-10-17 | 113.900 | 103.620 | 123.380 |
| 2023-10-18 | 116.730 | 107.250 | 126.810 |
| 2023-10-19 | 124.470 | 114.610 | 134.890 |
| 2023-10-20 | 132.550 | 122.790 | 142.890 |
| 2023-10-21 | 139.310 | 129.200 | 148.610 |
| 2023-10-22 | 134.740 | 125.400 | 144.300 |
Forecast Table
Based on the detailed forecast values provided, here is the period-by-period interpretation of the forecasts:
October 3, 2023 (112.49): The forecasted value for this date is within the confidence interval (CI) range.
October 4, 2023 (115.12): Similar to the first day, the forecasted value falls within the confidence intervals with an increase.
October 5-9, 2023: The forecasts continue to show an increasing trend, with values well within the confidence intervals.
October 10, 2023 (112.83): There is a slight decrease in the forecast compared to the previous day.
October 11-15, 2023: The values are relatively stable around 115-137, within the confidence intervals.
October 16, 2023 (119.3): A slight increase is observed compared to the previous day.
October 17-19, 2023: The forecasts are within the confidence intervals, but the values start to decrease slightly.
October 20, 2023 (132.55): A significant increase is seen in the forecast for this date.
October 21, 2023 (139.31): The forecast reaches its peak during this period.
October 22, 2023 (134.74): A decrease is observed after the peak, but the value remains within the confidence intervals.
Confidence Interval Analysis:
Special Attention Periods:
Overall, the forecasts show a mix of trends and fluctuations, with some periods requiring closer attention due to significant changes or uncertainty.
Forecast Table
Based on the detailed forecast values provided, here is the period-by-period interpretation of the forecasts:
October 3, 2023 (112.49): The forecasted value for this date is within the confidence interval (CI) range.
October 4, 2023 (115.12): Similar to the first day, the forecasted value falls within the confidence intervals with an increase.
October 5-9, 2023: The forecasts continue to show an increasing trend, with values well within the confidence intervals.
October 10, 2023 (112.83): There is a slight decrease in the forecast compared to the previous day.
October 11-15, 2023: The values are relatively stable around 115-137, within the confidence intervals.
October 16, 2023 (119.3): A slight increase is observed compared to the previous day.
October 17-19, 2023: The forecasts are within the confidence intervals, but the values start to decrease slightly.
October 20, 2023 (132.55): A significant increase is seen in the forecast for this date.
October 21, 2023 (139.31): The forecast reaches its peak during this period.
October 22, 2023 (134.74): A decrease is observed after the peak, but the value remains within the confidence intervals.
Confidence Interval Analysis:
Special Attention Periods:
Overall, the forecasts show a mix of trends and fluctuations, with some periods requiring closer attention due to significant changes or uncertainty.
Key Recommendations
Business Insights Key insights and recommendations based on the forecast
Business Insights
Based on the provided data profile, the forecast indicates an increasing trend with an average forecast value of 135.59 and an uncertainty range of 20.05 at a 95% confidence level.
Key Insights and Recommendations:
Trend Direction: The increasing trend suggests that demand or performance is on the rise. This could indicate growing market opportunities, customer interest, or operational efficiency.
Capacity Planning: With the trend heading upwards, it’s essential to assess current capacity levels. Consider investing in scalable infrastructure or workforce to meet the anticipated demand in the future.
Inventory Management: Given the upward trend, it’s advisable to maintain optimal inventory levels to prevent stockouts yet avoid overstock situations. Use data analytics to forecast demand accurately and align inventory levels accordingly.
Resource Allocation: Allocate resources effectively to support the increasing trend. This could involve hiring additional staff, investing in training programs, or upgrading tools and technology to enhance operational efficiency.
Risk Management: Acknowledge the uncertainty range of 20.05 and the confidence level of 95%. Develop contingency plans to address potential risks or disruptions that could affect the forecasted trend. Conduct scenario analysis to understand the impact of different outcomes within this range.
Monitoring and Adjustments: Continuously monitor key performance indicators against the forecasted values. Implement a feedback loop to adjust strategies in real-time based on emerging trends or deviations from the forecast.
By aligning capacity planning, inventory management, and resource allocation strategies with the forecasted trend, businesses can capitalize on opportunities for growth while effectively managing risks associated with uncertainty.
Business Insights
Based on the provided data profile, the forecast indicates an increasing trend with an average forecast value of 135.59 and an uncertainty range of 20.05 at a 95% confidence level.
Key Insights and Recommendations:
Trend Direction: The increasing trend suggests that demand or performance is on the rise. This could indicate growing market opportunities, customer interest, or operational efficiency.
Capacity Planning: With the trend heading upwards, it’s essential to assess current capacity levels. Consider investing in scalable infrastructure or workforce to meet the anticipated demand in the future.
Inventory Management: Given the upward trend, it’s advisable to maintain optimal inventory levels to prevent stockouts yet avoid overstock situations. Use data analytics to forecast demand accurately and align inventory levels accordingly.
Resource Allocation: Allocate resources effectively to support the increasing trend. This could involve hiring additional staff, investing in training programs, or upgrading tools and technology to enhance operational efficiency.
Risk Management: Acknowledge the uncertainty range of 20.05 and the confidence level of 95%. Develop contingency plans to address potential risks or disruptions that could affect the forecasted trend. Conduct scenario analysis to understand the impact of different outcomes within this range.
Monitoring and Adjustments: Continuously monitor key performance indicators against the forecasted values. Implement a feedback loop to adjust strategies in real-time based on emerging trends or deviations from the forecast.
By aligning capacity planning, inventory management, and resource allocation strategies with the forecasted trend, businesses can capitalize on opportunities for growth while effectively managing risks associated with uncertainty.
Key Takeaways and Recommendations
Key Recommendations
Business Insights Key insights and recommendations based on the forecast
Business Insights
Based on the provided data profile, the forecast indicates an increasing trend with an average forecast value of 135.59 and an uncertainty range of 20.05 at a 95% confidence level.
Key Insights and Recommendations:
Trend Direction: The increasing trend suggests that demand or performance is on the rise. This could indicate growing market opportunities, customer interest, or operational efficiency.
Capacity Planning: With the trend heading upwards, it’s essential to assess current capacity levels. Consider investing in scalable infrastructure or workforce to meet the anticipated demand in the future.
Inventory Management: Given the upward trend, it’s advisable to maintain optimal inventory levels to prevent stockouts yet avoid overstock situations. Use data analytics to forecast demand accurately and align inventory levels accordingly.
Resource Allocation: Allocate resources effectively to support the increasing trend. This could involve hiring additional staff, investing in training programs, or upgrading tools and technology to enhance operational efficiency.
Risk Management: Acknowledge the uncertainty range of 20.05 and the confidence level of 95%. Develop contingency plans to address potential risks or disruptions that could affect the forecasted trend. Conduct scenario analysis to understand the impact of different outcomes within this range.
Monitoring and Adjustments: Continuously monitor key performance indicators against the forecasted values. Implement a feedback loop to adjust strategies in real-time based on emerging trends or deviations from the forecast.
By aligning capacity planning, inventory management, and resource allocation strategies with the forecasted trend, businesses can capitalize on opportunities for growth while effectively managing risks associated with uncertainty.
Business Insights
Based on the provided data profile, the forecast indicates an increasing trend with an average forecast value of 135.59 and an uncertainty range of 20.05 at a 95% confidence level.
Key Insights and Recommendations:
Trend Direction: The increasing trend suggests that demand or performance is on the rise. This could indicate growing market opportunities, customer interest, or operational efficiency.
Capacity Planning: With the trend heading upwards, it’s essential to assess current capacity levels. Consider investing in scalable infrastructure or workforce to meet the anticipated demand in the future.
Inventory Management: Given the upward trend, it’s advisable to maintain optimal inventory levels to prevent stockouts yet avoid overstock situations. Use data analytics to forecast demand accurately and align inventory levels accordingly.
Resource Allocation: Allocate resources effectively to support the increasing trend. This could involve hiring additional staff, investing in training programs, or upgrading tools and technology to enhance operational efficiency.
Risk Management: Acknowledge the uncertainty range of 20.05 and the confidence level of 95%. Develop contingency plans to address potential risks or disruptions that could affect the forecasted trend. Conduct scenario analysis to understand the impact of different outcomes within this range.
Monitoring and Adjustments: Continuously monitor key performance indicators against the forecasted values. Implement a feedback loop to adjust strategies in real-time based on emerging trends or deviations from the forecast.
By aligning capacity planning, inventory management, and resource allocation strategies with the forecasted trend, businesses can capitalize on opportunities for growth while effectively managing risks associated with uncertainty.