To tackle this problem, you’ll need to perform a regression analysis using the last three independent variables:

1. x2 (Café) - number of stores that added a café wing.
2. x3 (Coupon Use) - percentage change in coupon use.
3. x4 (Magazine Perusal) - money lost each month from in-store magazine perusal.

The process involves running four separate regressions using different combinations of these variables as predictors of the dependent variable $y$ (Percentage Change).

Here’s a step-by-step guide for what you need to do:

Step 1: Prepare Data in Excel

1. Import the data into Excel from the file you've provided (or copy it manually if needed).
2. Select the relevant columns $y$, $x2$, $x3$, and $x4$.

Step 2: Set Up and Run Regressions

Run four different regression models with different combinations of variables:

1. Model 1: Use $x2$ and $x3$ as independent variables.
2. Model 2: Use $x2$ and $x4$ as independent variables.
3. Model 3: Use $x3$ and $x4$ as independent variables.
4. Model 4: Use all three variables $x2$, $x3$, and $x4$ as independent variables.

Step 3: Perform the Regressions in Excel

1. Go to Data > Data Analysis (you may need to enable the Data Analysis ToolPak if it's not already available).
2. Select Regression from the list.
3. Set y as the Dependent Variable (Percentage Change).
4. Set each combination of x2, x3, and x4 as the Independent Variables for each regression.
5. Record the R-squared values, p-values, and coefficients for each model.

Step 4: Analyze and Interpret Results

• R-squared: This value indicates how well the independent variables explain the variance in the dependent variable. A higher R-squared value means a better fit.
• P-values for the coefficients of each independent variable help assess if the variables are statistically significant predictors.
• Coefficient values: Assess the impact of each independent variable on the dependent variable.

Step 5: Conclusion

From the regression models, determine which combination of variables yields the highest R-squared and has statistically significant coefficients. This combination would be considered the "best" predictor of the percentage change in revenue sales.

Deliverables

• Excel Sheet: Show each regression output with R-squared, coefficients, and p-values.
• Write-up: Briefly explain which combination of variables provided the best prediction and why, based on the R-squared values and statistical significance.

Would you like further details on interpreting the regression results, or assistance with setting up the Excel file?

Relative Questions

1. What are R-squared and p-values, and how do they contribute to regression analysis?
2. How can you interpret a high or low R-squared in the context of predicting sales revenue?
3. Why is it important to check the statistical significance of each predictor variable?
4. What are potential limitations of using only three predictors in a regression model?
5. How would the interpretation change if some variables had low p-values but others did not?

Tip

Always check for multicollinearity among predictors when running multiple regressions. High multicollinearity can distort the importance of predictors in your model.