A sample of nine public universities and nine private universities was taken. The total cost for the year (including room and board) and the median SAT score (maximum total is 2400) at each school were recorded. It was felt that schools with higher median SAT scores would have a better reputation and would charge more tuition as a result of that. The data is in the table below. Use regression to help answer the following questions based on this sample data. Do schools with higher SAT scores charge more in tuition and fees? Are private schools more expensive than public schools when SAT scores are taken into consideration? Discuss how accurate you believe these results are using information related the regression models.
|
CATEGORY
|
TOTAL COST ($)
|
MEDIAN SAT
|
|
Public
|
21,700
|
1990
|
|
Public
|
15,600
|
1620
|
|
Public
|
16,900
|
1810
|
|
Public
|
15,400
|
1540
|
|
Public
|
23,100
|
1540
|
|
Public
|
21,400
|
1600
|
|
Public
|
16,500
|
1560
|
|
Public
|
23,500
|
1890
|
|
Public
|
20,200
|
1620
|
|
Private
|
30,400
|
1630
|
|
Private
|
41,500
|
1840
|
|
Private
|
36,100
|
1980
|
|
Private
|
42,100
|
1930
|
|
Private
|
27,100
|
2130
|
|
Private
|
34,800
|
2010
|
|
Private
|
32,100
|
1590
|
|
Private
|
31,800
|
1720
|
|
Private
|
32,100
|
1770
|