The linear regression model for predicting sales $y$ (in thousands of dollars) based on the week $x$ is:

$y = 683046 \cdot x - 2504759.273$

where:

• Slope $m = 683046$: This indicates that sales increase by approximately 683,046 thousand dollars (or 683 million dollars) each week.
• Intercept $b = -2504759.273$: This is the predicted sales at week zero, which isn’t meaningful in this context but is part of the model.

Residual Plot Analysis

The residual plot above shows a systematic pattern with increasing spread as $x$ increases, indicating the residuals are not randomly distributed around zero. This pattern suggests that a linear model may not be the best fit for the data, as it fails to capture the accelerating growth of sales.

Conclusion

This model does not appear to be a good fit due to the non-random distribution of residuals, which implies that sales might grow non-linearly over time (potentially exponentially).

Would you like further details on this analysis, or have any specific questions?

Related Questions

1. How would a non-linear regression model, like exponential growth, compare in fit for this data?
2. Can we calculate the correlation coefficient to quantify the linear fit strength?
3. How can we interpret residuals in evaluating other types of models?
4. What would the predictions look like for weeks beyond week 11 using this model?
5. Could polynomial regression improve the model's fit for accelerating trends?

Tip

A residual plot that shows a pattern often suggests the need to try a more complex model, such as polynomial or exponential regression.