=4-29 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 are in the following table. 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 to the regression models.

Category Total Cost ($) Median Sat Public 21,700 1990 Public 15,600 1620 Public 16,900 1810 Public 15,400 1540 Public 23,100 1540 Public 21,400 1600 Public 16,500 1560 Public 23,500 1890 Category Total Cost ($) Median Sat 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