# Regression/Confidence Intervals for Marketing Department

The marketing department of a large supermarket chain would like to determine the effect of shelf space devoted to pet food on the sales of pet food. A random sample of 12 equal-sized stores was selected, given below. The variables are weekly sales (in hundreds of dollars) and shelf space devoted to pet food (in square feet).

Store ShelfSpace_sqft WeeklySales_hundredsofdollars

1 5 1.6

2 5 2.2

3 5 1.4

4 10 1.9

5 10 2.4

6 10 2.6

7 15 2.3

8 15 2.7

9 15 2.8

10 20 2.6

11 20 2.9

12 20 3.1

1. Look at a plot of sales vs. shelf space. Does the relationship look linear?

2. Run a regression using weekly sales as the dependent variable and shelf space as the independent variable. Interpret the estimated slope.

3. Predict the average weekly sales (in hundreds of dollars) of pet food for stores with 8 square feet of shelf space for pet food.

4. Compute 90% confidence and prediction intervals for weekly sales of pet food for stores with 8 square feet of shelf space for pet food.

5. Explain the difference between the two intervals.

6. Can you prove at a 10% significance level that average sales, again for 8 square feet of shelf space, are more than $190?

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#### Solution Preview

1. Look at a plot of sales vs. shelf space. Does the relationship look linear?

Yes, the relationship looks linear.

2. Run a regression using weekly sales as the dependent variable and shelf space as the independent variable. Interpret the estimated slope.

I run the regression using excel. The results are attached in an separate excel file. The coefficient of slope is 0.074. We can interpret it as: for every additional feet of shelf space, we can expect that the ...

#### Solution Summary

The solution gives detailed steps on running a simple regression using excel and then analyzing further results such as building confidence intervals and prediction intervals for dependent variable.