Question

The owner of Gino’s Pizza restaurant chain believes that if a restaurant is located near a college campus, then there is a linear relationship between sales and the size of the student population. Suppose data are collected from a sample of n = 10 Gino’s Pizza restaurants located near college campuses with the following reported sample statistics:

	X= Population (1000s)	Y = Sales ($1000s)
Sample Mean	14	130
Sample Standard Deviation	7.944	41.806
Sample Variance	63.111	1747.778
Sample Covariance	315.556

We want to find the equation of the least-squares regression line predicting quarterly pizza sales (y) from student population (x).

1. Estimate and interpret the sample correlation between population and sales.

2. Estimate the slope of the linear regression equation of Sales on Population where Population is the dependent variable.

3. Estimate the intercept of the linear regression equation of Sales on Population where Population is the dependent variable.

4. Compute the Total Sum of Squares (SST)

5. Compute the Regression Sum of Squares (SSR)

6. Compute the Error Sum of Squares (SSE)

7. Complete the ANOVA Table for Regression

Source of Variation	SS	df	MS	F
Regression
Error
TOTAL

1. What is the standard error for the slope estimate?

2. Develop a 95% confidence interval estimate for β₁.

3. Test for the Significance of β₁. Use α = 0.05

4. Use an F-test to determine if the regression model is significant.

5. Compute the R² and interpret.

6. Develop a 95% Prediction Interval for a single location that has a student population of 17.

7. Develop a 95% Confidence Interval for the average Sales for a group of locations where the student population is 17.

Answer 1