Question

6. (6 points) Graduation rates and what influences them have become a concern in colleges and universities. The predictor variables used are student-to-faculty ratio, percentage of freshmen in the top 10% of their high school class, and percentage of applicants accepted. The multiple regression analysis was done for a sample of 48 schools. Coef Predictor Constant STD/FAC TOP 10%HS ACCEPTED 97.9 0.01429 -0.29255 -0.2128 SE Coef 5.530 0.05727 0.05199 0.2033 T P 17.700.000 0.25 0.804 -5.63 0.000 - 1.050.301 S = 5.138 R-Sq = 63.8% R-Sq(adj) = 61.3% Analysis of Variance DF 3 Source Regression Residual Error Total SS 2045.79 1161.46 3207.25 MSFP 681.93 25.83 0.000 26.40 For each of the predictor variables state the null and alternate hypotheses, the test statistic, the p-value, and hypothesis test conclusion and interpretation.

(Be sure to show ALL work where applicable!)

Student-to-faculty ratio:

Top 10% of HS graduating class:

Percentage of applicants accepted:

Answer 1

Independent variables	Coefficients
Student-to-faculty ratio:	0.01429
Top 10% of HS graduating class:	-0.29255
Percentage of applicants accepted:	-0.2128

Hypothesis for predictor variables

H0: βi = 0

Ha: βi not = 0

Independent variables	T value (b/SE)	P value(From t table)		Alpha(Assume)	Significant
Student-to-faculty ratio:	0.25	0.804	>	0.05	No
Top 10% of HS graduating class:	-5.63	0	<	0.05	Yes
Percentage of applicants accepted:	-1.05	0.301	>	0.05	No

Interpretation:

Student-to-faculty ratio:

If Student-to-faculty ratio is increases by 1 Unit, Then Dependent variable increases by 0.25 units with other independent variables held constant

Top 10% of HS graduating class:

If Top 10% of HS graduating class is increases by 1 Unit, Then Dependent variable decreases by 5.63 units with other independent variables held constant

Percentage of applicants accepted:

If Percentage of applicants accepted is increases by 1 Unit, Then Dependent variable decreases by 1.05 units with other independent variables held constant