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.

Regression, Part 1

Jamie asks: When you did blogs on several of the statistical analyses, you did not do one on regression. Would that be one you would consider blogging about? I've been getting stuck on that.  

Of course, Jamie! I am going to assume that you are interested in multiple regression. This is a little more complicated to try to cover in a blog post, but let's give it a try! Multiple regression is a more sophisticated extension of correlation and is used when you want to explore the predicative ability of a set of independent variables (IV) on one continuous dependent measure (DV). There are different types of multiple regression that allow you to compare the predictive ability of particular independent variables ad find the best set of variables to predict a dependent variable. I will be looking at a standard multiple regression. 

An example might be the time to complete an exam (IV₁), the person's grade on the exam (IV₂), and perceived stress (DV). Our research questions are – 1) How well does time on the exam and grade on exam predict perceived stress? How much variance in perceived stress scores can be explained by scores on these two IVs? 2) Which is the best predictor of perceived stress: time or grade? 

Let's do an example of a multiple regression together. So open SPSS, first go to Edit on the menu, select Options and make sure there is a check in the box No scientific notation for small numbers in tables. Enter the following data for your sample: 

Under Variable view (see tab at bottom of page), It should look like: 

Name	Type	Width	Decimals	Label	Values	Ignore the rest
Examtime	numeric	8	0	Time to complete exam	None	Ignore the rest
Grade	numeric	8	0	Exam grade	None	Ignore the rest
Stress	numeric	8	0	Perceived stress	None	Ignore the rest

 

Go back to Data View and enter the following: 

Examtime	Grade	Stress
20	63	85
45	89	65
36	75	82
59	92	45
56	96	50
27	66	90
39	70	77
52	89	70
43	82	85
55	99	47

 

Go to Analyze/ Regression/Linear. Move your continuous DV (stress) into the Dependent box. 

Move your IVs (exam time and grade) into the independent box 

For Method, make sure Enter is selected.

Click on the Statistics button

             Select the following: Estimates, Confidence Intervals, Model fit, Part and partial correlations, and Collinearity diagnostics

             In the Residuals section, select Casewise diagnostics and Outliers outside 3 standard deviations. Click on Continue.

Click on the Plots button

             Click on *XRESID and move to the Y box

             Click on *ZPRED and move to the X box

In the section labeled Standardized Residual Plots, tick the normal probability plot option. Click on continue

Click on the Save button

             In the section labeled Distances, select Mahalanobis box and Cook's

Click on Continue and then OK 

Next time we will look at the output and interpretation. 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