Answer:
a) Interpret the results and determine whether or not the coefficients are significantly dif- ferent fromzero. Do the coefficients have the expected sign?
An increase in reputation by one category, increases the cost by
roughly $3,985. The larger the size of the college/university, the
lower the cost. An increase of 10,000 students results in a $2,000
lower cost. Private schools charge roughly $8,406 more than public
schools. A school with a religious affiliation is approximately $2,376
cheaper, presumably due to subsidies, and a liberal arts college also
charges roughly $416 less. There are no observations close to the
origin, so there is no direct interpretation of the intercept. Other than
perhaps the coefficient on liberal arts colleges, all coefficients have
the expected sign.
(b) What is the forecasted cost for a liberal arts college, which has no religious affiliation, a size of 1,500 students and a reputation level of 4.5? (All liberal arts colleges are private.)
7,311.17 + 3,985.20×4.5 – 0.20×1500
+ 8,406.79×1 – 416.38×1 – 2,376.51×0=$ 32,935
(c) Suppose that you switch from a private university to a public university, which has a ranking tha's 0.5 lower and 10,000 more students. What is the effect on your cost?
Roughly $ 12,400. Since over the four years of education, this
implies approximately $50,000, it is a substantial amount of money
for the average household.
(d) What is the p-value for the null hypothesis that the coefficient on Size is equal to zero? Based on this, should you eliminate the variable from the regression? Why or why not?
Using a one-sided alternative hypothesis, the p-value is 6.2 percent. Variables should not be eliminated simply on grounds of a statistical test. The sign of the coefficient is as expected, and its magnitude makes it important. It is best to leave the variable in the regression and let the reader decide whether or not this is convincing evidence that the size of the university matters
(e) You want to test simultaneously the hypotheses ha and bert - 0. Your regression package returns an F-statistic of 1.23. Can you reject the null hypothesis?
The critical value for F2,∞ is 3.00 (5% level) and 4.61 (1% level). Hence you cannot reject the null hypothesis in this case
(f) Eliminating the Size and Dlibartvariables from your regression, the estimated regression becomes 5,450.35+3,538.84 .
Reputation 1,772.35 (590.49) cost 10,935-70.Dpriv-2, 783.31-Dreligion 575.51) (1,150.57) R20.72 SER- 3,792.68 Why do you think that the effect of attending a private institution has increased now?
Step-by-step explanation:
a.An increase in reputation by one category, increases the cost by
roughly $3,985. The larger the size of the college/university, the
lower the cost. An increase of 10,000 students results in a $2,000
lower cost. Private schools charge roughly $8,406 more than public
schools. A school with a religious affiliation is approximately $2,376
cheaper, presumably due to subsidies, and a liberal arts college also
charges roughly $416 less. There are no observations close to the
origin, so there is no direct interpretation of the intercept. Other than
perhaps the coefficient on liberal arts colleges, all coefficients have
the expected sign.
b.7,311.17 + 3,985.20×4.5 – 0.20×1500
+ 8,406.79×1 – 416.38×1 – 2,376.51×0=$ 32,935
c.Roughly $ 12,400. Since over the four years of education, this
implies approximately $50,000, it is a substantial amount of money
for the average household.
d.Using a one-sided alternative hypothesis, the p-value is 6.2 percent. Variables should not be eliminated simply on grounds of a statistical test. The sign of the coefficient is as expected, and its magnitude makes it important. It is best to leave the variable in the regression and let the reader decide whether or not this is convincing evidence that the size of the university matters
e.The critical value for F2,∞ is 3.00 (5% level) and 4.61 (1% level). Hence you cannot reject the null hypothesis in this case
