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.

= .95  There is high or a true correlation between sales of pizza and student population. Because of high correlation, an upward slope linear relationship between x and y exists.

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)

Answer 1

(a)

Sample correlation coefficient

square root of {sample covariance / (product of sample standard deviations)} = 0.97

The high positive value of correlation means, that there is a high linear relationship between pizza sales and student population. If the student population increases, the quarterly pizza sales also increase.

(b) Estimate of slope = (n * sample covariance) / (n * sample variance of x) = 5

(c) Estimate of intercept = (sample mean of y) - (estimate of slope * sample mean of x) = 130 - (5*14) = 60

(d) Total Sum of Squares = = (n * sample variance of y) = 10 * 1747.778 = 17477.78