# Class_19 - Significance Tests for Regression Models and...

• Notes
• 22
• 100% (1) 1 out of 1 people found this document helpful

This preview shows pages 1–6. Sign up to view the full content.

Significance Tests for Regression Models and Their Coefficients

This preview has intentionally blurred sections. Sign up to view the full version.

A. Testing the Significance of the Regression Coefficient The null hypothesis in the significance test for the regression coefficient (i.e., slope) is: H 0 : β = 0.0 This simple symbolic expression says more than might first appear. It says: If we begin by assuming that there is no relationship between X and Y in general (i.e., in the universe from which our sample data come), then how likely is it that we would find a regression coefficient for our sample to be DIFFERENT FROM 0.0? Put the other way around, if we find a relationship between X and Y in the sample data, can we infer that there is a relationship between X and Y in general?
To test this null hypothesis, we use our old friend the t-test: where the standard error is: b b t σ β ˆ - = ( 29 1 ˆ 2 - = N s MS X Error b σ

This preview has intentionally blurred sections. Sign up to view the full version.

This is the standard deviation of the sampling distribution of all theoretically possible regression coefficients for samples of the same size drawn randomly from the same universe. Recall that the mean of this sampling distribution has a value equal to the population characteristic (parameter), in this case the value of the regression coefficient in the universe. Under the null hypothesis, we initially assume that this value is 0.0. To test the significance of the regression coefficient (and the model as a whole), we need the statistical information found in the usual analysis of variance summary table. We already have most of this information for our previous example.
Recall that R 2 YX , the Coefficient of Determination, was found from R 2 YX = SS Regression / SS Total From our time/temperature example, remember that R 2 YX was 0.999. Total sum of squares can be found from SS Total = s Y 2 (N - 1) From our previous calculations, remember that s Y 2

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.
• Fall '07
• Velez
• Regression Analysis, Null hypothesis, regression coefficient, variance summary table

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern