Question

What will be the final regression model formed from regression with the stepwise predictor selection method? Please specify the actual value(s) of the parameter estimate(s) in the model.

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	35.383	4.911		7.204	.000
	GREQ	.064	.008	.787	8.359	.000
2	(Constant)	27.927	4.556		6.130	.000
	GREQ	.055	.007	.668	7.838	.000
	AR	3.940	.950	.353	4.147	.000
3	(Constant)	23.231	4.654		4.992	.000
	GREQ	.037	.010	.450	3.854	.000
	AR	3.715	.897	.333	4.142	.000
	MAT	.269	.105	.297	2.568	.014
a. Dependent Variable: GPA

Answer 1

This is kind of hierarchical step wise regression with three steps. In this kind of regression modelling we wants to see whether the added a new variable is significant in the model.

After adding the variable in each step, the the significance p-value for each variable is recorded to determine whether the variable significantly explains the dependent variable.

And the standardized coefficients are used to compare the relative importance of of each coefficient.

There are 3 models are created and the variables are added in step 2 and step 3.

For step 1: Model 1:

Dependent variable (DV): GPA, Independent Variable (IV): GREQ

Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	35.383	4.911		7.204	0.000
	GREQ	0.064	0.008	0.787	8.359	0.000

For IV GREQ, the beta value represents the coefficient of IV in the regression equation and the coefficient is significant at the 99.9% level of confidence ( or say 0.001% significance level, ***P< 0.001)

The Standardized Coefficients beta = 0.787.

For step 2: Model 2:

Dependent variable (DV): GPA, Independent Variables (IVs): GREQ and AR.

Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
2	(Constant)	27.927	4.556		6.13	0.000
	GREQ	0.055	0.007	0.668	7.838	0.000
	AR	3.94	0.95	0.353	4.147	0.000

For IV GREQ, the beta value is significant at the 99.9% level of confidence ( or say 0.001% significance level, ***P< 0.001)

The Standardized Coefficients beta = 0.668.

For IV AR, the beta value is significant at the 99.9% level of confidence ( or say 0.001% significance level, ***P< 0.001)

The Standardized Coefficients beta = 0.353.

The IV AR is relatively less important compare to IV GREQ.

For step 3: Model 3:

Dependent variable (DV): GPA, Independent Variables (IVs): GREQ, AR and MAT

Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
3	(Constant)	23.231	4.654		4.992	0.000
	GREQ	0.037	0.01	0.45	3.854	0.000
	AR	3.715	0.897	0.333	4.142	0.000
	MAT	0.269	0.105	0.297	2.568	0.014

For IV GREQ, the beta value is significant at the 99.9% level of confidence ( or say 0.001% significance level, ***P< 0.001)

The Standardized Coefficients beta = 0.45.

For IV AR, the beta value is significant at the 99.9% level of confidence ( or say 0.001% significance level, ***P< 0.001)

The Standardized Coefficients beta = 0.33.

For IV MAT, the beta value is significant at the 90.0% level of confidence ( or say 0.10% significance level, *P< 0.1)

The Standardized Coefficients beta = 0.297.

Relatively importance => GREQ > AR > MAT