econometrics

answer ALL questions and show ALL work

The management of Armand?s Pizza Parlors, a chain ofItalian-food restaurants located in a 5-state area, is currentlyfacing a problem. One of the most successful types of locations forArmand?s has been near a college campus.

Prior to opening a new restaurant Armand?s management requiresan estimate of yearly sales revenues. Such an estimate is used inplanning the appropriate restaurant capacity, making initialstaffing decision, and deciding whether or not the potentialrevenues justify the cost of operation.

Suppose management believes that the size of the studentpopulation on the nearby campus is related to the annual salesrevenues. On an intuitive basis, management believes restaurantslocated near larger campuses generate more revenue than those nearsmall campuses. To evaluate the relationship between studentpopulation and annual sales, Armand?s collected data from a sampleof 10 of its restaurants located near college campuses.

1. Calculate and interpret the correlation coefficient betweenstudent population and annual sales.

2. Write the population regression equation. Write the sampleregression equation. What is the difference between the two interms of notation?

3. Write the estimated regression equation. Interpret thecoefficients.

4. Calculate SSR, SSE, and SST. What does each of thesemean?

5. Calculate and interpret the coefficient of determination.What are the issues with the coefficient of determination? How arethese issues addressed?

Data on Student Population and Annual Sales for Ten Armand's Restaurants Restaurant 1 NM in 1000 2 3 4 5 6 7 8 9 10 Student Population (1,000's) N 10 00 00 N 2 6 8 8 12 16 2 NIN 2 22 26 Annual Sales ($1,000's) 58 105 88 118 117 137 157 169 149 202