The Admission director for a college far from mart and town believes that an inverse relationship exists between a private college's average discount rate(determined by the average amount of scholarships students receive) and the annual yield (the percentage of admitted students who actually attend). The Director's independent variable is a private college's discount rate measured as a percentage, and the dependent variable is the college's annual yield measured as a percentage. The following results were obtained for a sample of 30 private colleges: x- Discount rate(percentage) - range: 35 to 72 percent y- Annual Yield(percentage) - range: 12 o 81 percent Σxi = 1612 Σyi = 898 Σxiyi = 44,377 Σxi2 = 89,790 Σyi2 = 35,704 a. Calculate the sample regression line's slope estimate. Interpret the sample regression line's slope estimate. b. Calculate the sample regression line's intercept estimate. Interpret the sample regression line's intercept estimate. Assume the following sum of squares: SST = 8,824 SSR = 4,736 SSE = 4,088 c. Calculate the standard error of estimate. Interpret the standard error of estimate. d. Calculate the coefficient of determination. Interpret the coefficient of determination. Assume the estimated standard deviation of b1 equals: sb1 = 0.2145 The director believes that a significant negative linear relationship exists between a private college's discount rate and its annual yield. Based upon the sample results that were obtained, test the directors claim using a slope estimate. e. State the null and alternative hypothesis. f. What is the appropriate test statistic. g. Determine the critical value(s) for this test using a 1% significance level. h. Calculate the value of the test statistic. i. What is your decision and conclusion?
The Admission director for a college far from mart and town believes that an inverse relationship exists between a private college's average discount rate(determined by the average amount of scholarships students receive) and the annual yield (the percentage of admitted students who actually attend). The Director's independent variable is a private college's discount rate measured as a percentage, and the dependent variable is the college's annual yield measured as a percentage. The following results were obtained for a sample of 30 private colleges:
x- Discount rate(percentage) -
y- Annual Yield(percentage) - range: 12 o 81 percent
Σxi = 1612
Σyi = 898
Σxiyi = 44,377
Σxi2 = 89,790
Σyi2 = 35,704
a. Calculate the sample regression line's slope estimate. Interpret the sample regression line's slope estimate.
b. Calculate the sample regression line's intercept estimate. Interpret the sample regression line's intercept estimate.
Assume the following sum of squares:
SST = 8,824
SSR = 4,736
SSE = 4,088
c. Calculate the standard error of estimate. Interpret the standard error of estimate.
d. Calculate the coefficient of determination. Interpret the coefficient of determination.
Assume the estimated standard deviation of b1 equals:
sb1 = 0.2145
The director believes that a significant negative linear relationship exists between a private college's discount rate and its annual yield. Based upon the sample results that were obtained, test the directors claim using a slope estimate.
e. State the null and alternative hypothesis.
f. What is the appropriate test statistic.
g. Determine the critical value(s) for this test using a 1% significance level.
h. Calculate the value of the test statistic.
i. What is your decision and conclusion?
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