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 independent variable.

3. Estimate the intercept of the linear regression equation of Sales on Population where Population is the independent 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)

Answer 1

SSxx =    Σ(x-x̅)² = variance of x * (n-1) =   63.111*9 = 567.9990

SSyy = Σ(y-ȳ)² = variance of y * (n-1) = 1747.778*9 = 15730.00

SSxy=   Σ(x-x̅)(y-ȳ) = covariance*(n-1) = 315.556*9 = 2840.00

a)

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.9501

there is a strong postive correlation between x and y

b) estimated slope , ß1 = SSxy/SSxx =   2840.0   /   567.999   =   5.00

c) intercept,   ß0 = y̅-ß1* x̄ =   59.99978 ≈ 60

d) SST =SSyy = 15730.00

e) SSR=   S²xy/Sxx =   14200.065

f) SSE=   (SSxx * SSyy - SS²xy)/SSxx =    1529.9370