Question

The standard project is to use multiple regression analysis to analyze a data set. 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.

a. The estimated multiple regression analysis equation. b. Does the model work? Research this question, use the Significance F value and compare it using p-value. c. How well does the model work? Research this question using p-values and R Square. d. Which variables contribute to the model? Research this question using p-values. e. General interpretation of the data and the data analysis.

Regression Statistics
Multiple R	0.422451381
R Square	0.178465169
Adjusted R Square	0.148037953
Standard Error	0.431974891
Observations	113
ANOVA
	df	SS	MS	F	Significance F
Regression	4	4.377924324	1.094481081	5.86531378	0.000260992
Residual	108	20.15304913	0.186602307
Total	112	24.53097345
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	0.327601267	0.33188857	0.9870821	0.325808653	-0.330259456	0.985461991	-0.330259456	0.985461991
Gender	-0.30076921	0.083982457	-3.581333792	0.000513969	-0.467237009	-0.134301411	-0.467237009	-0.134301411
Age	0.006147102	0.09460487	0.064976589	0.94831276	-0.181376164	0.193670367	-0.181376164	0.193670367
GPA	0.165452103	0.054477398	3.037077944	0.002995123	0.05746845	0.273435756	0.05746845	0.273435756
Total Q	0.000365667	0.003539872	0.103299547	0.917916809	-0.006650973	0.007382307	-0.006650973	0.007382307

Answer 1

Part a )
The regression equation is :

Enrollment status = 0.3276-0.3008*Gender+0.006147*Age+0.1655*Gpa+0.000366*TotalQ

The coefficient values are obtained from the following part of the output:

.

part b)

The model got F value = 5.8653 and a P value = 0.000261

Since the P value 0.000261 < alpha 0.05 , this implies that the model has a significant effect in predicting the value of enrollment status

.

Part c)

The P value obtained suggest that the model is significant in predicting the values of the response variable

But the value of r square = 0.1785 ( rounded to 4 decimal values) is very small

A r square value 0.1785*100 = 17.85% implies that the model is able to explain on 17.85% of the variation in the value of the response variable

Hence in true sense though the model is statistically significant , it doesnot actually help is explaining the variation in the response variable student enrollment status

.

Part d)

The variables with P value < 0.05 contribute to the model significantly

Hence variables: Gender and GPA have got the respective P values < 0.05., hence they have significant influence on the model

The variables: Age and Total Q have respectively a larger p value > 0.05 , hence they so not have significant influence on the model

.

Part e)

Total 113 observations are taken to predict the relation of response variable enrollment status based on the independent variables, age, gender , GPA and Total Q. The P value obtained for model is 0.000261 with F value 5.8653 thus indicating that the model is significant. If we observe the variables individually, once can observe that P values for Gender and GPA are less than 0.05 thus indicating that these variables have significant influence on the model. The R square value of the model is : 17.85% which implies only 17.85% of the variation in the enrollment status is explained by this model.