Regression, Part 2

Last time we ran a regression analysis, this time we will look at the output and interpretation. Your results should look like the following:

Descriptive Statistics
				Mean		Std. Deviation			N
perceived stress				69.60		17.063			10
Time to complete exam				43.20		12.925			10
exam grade				82.10		12.879			10
Model Summaryb Model R R Square Adjusted R Square Std. Error of the Estimate 1 .884a .781 .718 9.056 a. Predictors: (Constant), exam grade, Time to complete exam b. Dependent Variable: perceived stress   Correlations   perceived stress Time to complete exam exam grade Pearson Correlation perceived stress 1.000 -.868 -.874 Time to complete exam -.868 1.000 .943 exam grade -.874 .943 1.000 Sig. (1-tailed) perceived stress . .001 .000 Time to complete exam .001 . .000 exam grade .000 .000 . N perceived stress 10 10 10 Time to complete exam 10 10 10 exam grade 10 10 10   ANOVAa Model Sum of Squares df Mean Square F Sig. 1 Regression 2046.264 2 1023.132 12.474 .005b Residual 574.136 7 82.019     Total 2620.400 9       a. Dependent Variable: perceived stress b. Predictors: (Constant), exam grade, Time to complete exam   Coefficientsa
Model		Unstandardized Coefficients			Standardized Coefficients		t	Sig.		95.0% Confidence Interval for B			Correlations			Collinearity Statistics
		B	Std. Error		Beta					Lower Bound	Upper Bound		Zero-order	Partial	Part	Tolerance	VIF
1	(Constant)	146.784	31.053				4.727	.002		73.354	220.214
	Time to complete exam	-.518	.702		-.393		-.739	.484		-2.177	1.141		-.868	-.269	-.131	.111	9.025
	exam grade	-.667	.704		-.504		-.948	.375		-2.332	.998		-.874	-.337	-.168	.111	9.025
a. Dependent Variable: perceived stress

There are many aspects that can be checked, based on the analyses we have run; however, I do not have the space to review them all. Please see Pallant (2013) for an in-depth discussion of them. 

Let's evaluate our model. Look in the Model Summary box and check the value under the heading R Square. This tells you how much of the variance in the DV (stress) is explained by the model (which includes the IVs exam time and grades). In this case, the value is .781 (see yellow highlight), so we can say that the model explains 78.1% of the variance in perceived stress. We had a very small sample, however, so it is best to use the adjusted R square .718 or 71.8%, which is a better estimate. To assess the statistical significance of the result, we need to look at the table labeled ANOVA. This tests the null hypothesis that multiple R in the population equals 0. In our example, the model reaches statistical significance of .005 (see blue text).  

Next, take a look at the table of Coefficients and the column labeled Beta. Ignoring any negative signs we can see that exam grade made the largest contribution (.504) to explaining the DV, when the variance explained by all other variables are controlled. The Beta value for exam time was slightly lower (.393) indicating it made less of a contribution (see red text) 

The results of the analyses allow us to the answer the two questions we posed at the beginning. The model, which includes the time to complete the exam and grade, explains 71.8% of the variance in perceived stress. Of these two variables, exam grade makes the largest contribution (beta = -.504), although exam time also made a statistically significant contribution (beta = -.393).

Next time we will look at the formation of research questions. Do you have an issue or a question that you would like me to discuss in a future post? Would you like to be a guest writer? Send me your ideas! Send me an email with your ideas. leann.stadtlander@waldenu.edu 

Pallant, J. (2013). The SPSS Survival Manual, 5^th edition. Open University Press.