Question

A sample of 18 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.

University	Total cost ($)	Median SAT
1	21,700	1980
2	15,600	1890
3	16,900	1990
4	15,400	1660
5	23,100	1810
6	21,400	1600
7	16,500	1560
8	23,500	2130
9	20,200	2010
10	30,400	1720
11	41,500	1550
12	36,100	1770
13	42,100	1790
14	27,100	2010
15	34,800	2130
16	28,100	1970
17	32,100	1980
18	31,800	1640

*Level of significant is 0.05

Use regression to help answer the following question based on the sample data;
a) Develop regression model and predict the total cost if median SAT equal to 1700?
b) Can we rely on regression model from (a)? why? And is there any relationship
between SAT and cost?

Answer 1

The regression model developed is:

Total Cost = 33414.04 - 3.7105 * Median SAT

where the intercept and the slope values have been calculated using the formula:

Thus for a Median SAT score of 1700 the Total cost is $27106.13

No we cannot rely the regression model from (a) since, the p-value of the regression is 0.7441 which is much higher than 0.05. Hence there is not significant evidence at 5% level of significance that there exists a linear relationship between median SAT score and total cost.

In fact from the regression model one can observe that higher the SAT score less is the cost of the school which contradicts the earlier statement that as the median SAT score increases the cost also increases.

From the results one can deduce a negative relationship between Median SAT and total cost, which is not significant at 5% level of significance.