The linear regression model for the given data yields the following equation:

$y = -8650.836x + 89354.836$

where:

• Slope ($m$) = $-8650.836$
• Intercept ($b$) = $89354.836$

The residual plot above shows the distribution of residuals around the week number. Ideally, for a good model fit, the residuals should be randomly scattered around the horizontal axis (at zero). Here, there is a noticeable pattern, suggesting that the linear model may not perfectly fit the data, especially since the residuals increase and decrease in a somewhat systematic way. This could imply that a different model, possibly a non-linear one, might better capture the trend.

Would you like further details on the model, or do you have any questions?

Here are some additional questions you may find helpful:

1. How does the residual pattern suggest a potential misfit for the linear model?
2. Can we try a different type of regression model to fit this data?
3. What effect does the large negative slope have on future predictions for sales?
4. How might we interpret the intercept value in the context of week zero?
5. What other statistical tests could we perform to assess the fit of this model?

Tip: Checking residual plots is a quick and effective way to visually assess the fit of a regression model.