Question

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.4331416
R Square	0.187611646
Adjusted R Square	0.162024611
Standard Error	0.433172316
Observations	132
ANOVA
	df	SS	MS	F	Significance F
Regression	4	5.503274937	1.375818734	7.332293373	2.40454E-05
Residual	127	23.8300584	0.187638255
Total	131	29.33333333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	0.25853498	0.277463085	0.931781539	0.353217396	-0.290514392	0.807584352	-0.290514392	0.807584352
Gender	-0.25814087	0.076988473	-3.352980767	0.001053904	-0.410487164	-0.105794575	-0.410487164	-0.105794575
Age Range	-0.013475664	0.087855561	-0.153384299	0.878338675	-0.187325965	0.160374637	-0.187325965	0.160374637
GPA	0.158322458	0.038484989	4.113875582	6.94533E-05	0.08216761	0.234477307	0.08216761	0.234477307
Total Q	0.001279543	0.003172196	0.403361987	0.687360239	-0.00499766	0.007556746	-0.00499766	0.007556746

The data set is a study of student persistent enrolling in the next semester based on Gender, Age, GPA, a 22 questionnaire on self-efficacy, and student enrollment status.The educational researcher wants to study the relationship between student enrollment status as it relates to gender, age, GPA, and the total response to a 22 questionnaire survey.

2. The estimated multiple regression analysis equation.

3. Does the model work?

4. How well does the model work?

5. Which variables contribute to the model?

6. General interpretation of the data and the data analysis

Answer 1

2 The estimated multiple regression analysis equation is

Y(hat)= 0.258-0.258*Gender - 0.013*Age range+ 0.158* GPA+0.001*total Q

3) Yes model work. Because P value from ANOVA table is 0.000024 which is significant at 0.05 level of significance.

4) R square is 0.1876 which means 18.76 % indicates that the model explains 18.76% of the variability of the response data around its mean.

5) Gende and GPA contribute to the model

Reason: Because these variable p value are significant which means less than 0.05 level of significance.

6) The students persistent enrolling in next semester is predicted by using Gender, age, GPA and Total Q. Sample size is large . So we can assume that data is normally distributed. Standard error of regression is 0.433 which is very small. S represents the average distance that the observed values fall from the regression line. Smaller values are better because it indicates that the observations are closer to the fitted line.