Question

The data shown below indicate the average tuition (in dollars) over a six-year period for private and public colleges in a region Complete parts a through below Us 001 where ne Year 1 2 3 4 5 6 Private 8,752 9,082 12.277 13,379 15 627 18,398 Public 2010 2.308 3,169 3,649 4,616 5,652 Conduct a simple linear regression analysis of these data in which the average tuition for private colleges is predicted by the average public college tuition Test the significanc What is the estimated regression slope coefficient? -- (Round to two decimal places as needed) What is the estimated regression intercept? -- (Round to the nearest whole number as needed) test the significance, first determine the hypotheses to test. Choose the correct answer below. Ос. OB. Ho By 0 D A. Ho Be to HA B,> 0 HAB=0 OF D. Ho By > 0 O E. Ho B0 Hai By 20 HAB, SO the test statistic t for a=0.01. Select the correct choice below and fill in any answer boxes to complete your choice

Answer 1

The Data Set

Year	Private	Public
1	8752	2010
2	9082	2308
3	12277	3169
4	13379	3649
5	15627	4616
6	18398	5652

The regression analysis (done in Excel Data > Data Analysis > Regression)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.996611538
R Square	0.993234558
Adjusted R Square	0.991543197
Standard Error	344.2407229
Observations	6

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 99.0%	Upper 99.0%
Intercept	3325.620196	420.0915336	7.916418042	0.001377824	2159.259113	4491.981278	1391.47892	5259.761471
Public	2.689276716	0.110975648	24.23303466	1.72031E-05	2.381158922	2.99739451	2.178334306	3.200219126

1. Slope Coeeficient: 2.69

2. Intercept: 3325.62

3.

$H_0: \beta = 0$

$H_a: \beta \ne 0$

4. t < 2.18 and t > 3.20

5. t statistic is 24.23

6. Since t statistic > 3.20, we reject the null hypothesis

7. The regression line is

Private = 3325.62 + 2.69 * Public

When Public = 100

Private = 3325.62 + 2.69 * 100 = 3594.62

8. When Public = 6500

Private = 3325.62 + 2.69 * 6500 = 20810.62