The results of the linear regression analysis are as follows:

• Slope (m): 21773.036 (rounded to three decimal places)
• Intercept (b): -70199.400 (rounded to three decimal places)
• $R^2$ value: 0.695, indicating that about 69.5% of the variance in sales is explained by the week variable.

Model Equation

The equation of the linear model is: $\text{Sales (y)} = 21773.036 \times \text{Week (x)} - 70199.400$

Residual Plot Analysis

The residual plot shows some pattern rather than a random scatter, indicating that a linear model may not be the best fit for this data. A non-linear model might better capture the relationship between the weeks and sales values.

Would you like more details on any part of this analysis?

Here are some questions to explore further:

1. What does a residual plot tell us about the fit of a model?
2. How is the $R^2$ value interpreted in the context of model fit?
3. How could we improve the model if linear regression isn’t a good fit?
4. What other types of models might work better for this dataset?
5. How would you calculate the prediction for a specific week using this model?

Tip: When interpreting residuals, look for randomness; any pattern in residuals suggests that the model may be missing some aspect of the relationship between variables.