{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# ch06 - Multiple Regression Analysis y = 0 1x1 2x2 kxk u 4...

This preview shows pages 1–8. Sign up to view the full content.

Economics 20 - Prof. Anderson 1 Multiple Regression Analysis y = β 0 + β 1 x 1 + β 2 x 2 + . . . β k x k + u 4. Further Issues

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

View Full Document
Economics 20 - Prof. Anderson 2 Redefining Variables Changing the scale of the y variable will lead to a corresponding change in the scale of the coefficients and standard errors, so no change in the significance or interpretation Changing the scale of one x variable will lead to a change in the scale of that coefficient and standard error, so no change in the significance or interpretation
Economics 20 - Prof. Anderson 3 Beta Coefficients Occasional you’ll see reference to a “standardized coefficient” or “beta coefficient” which has a specific meaning Idea is to replace y and each x variable with a standardized version – i.e. subtract mean and divide by standard deviation Coefficient reflects standard deviation of y for a one standard deviation change in x

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

View Full Document
Economics 20 - Prof. Anderson 4 Functional Form OLS can be used for relationships that are not strictly linear in x and y by using nonlinear functions of x and y – will still be linear in the parameters Can take the natural log of x, y or both Can use quadratic forms of x Can use interactions of x variables
Economics 20 - Prof. Anderson 5 Interpretation of Log Models If the model is ln( y ) = β 0 + β 1 ln( x ) + u β 1 is the elasticity of y with respect to x If the model is ln( y ) = β 0 + β 1 x + u β 1 is approximately the percentage change in y given a 1 unit change in x If the model is y = β 0 + β 1 ln( x ) + u β 1 is approximately the change in y for a 100 percent change in x

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

View Full Document
Economics 20 - Prof. Anderson 6 Why use log models? Log models are invariant to the scale of the variables since measuring percent changes They give a direct estimate of elasticity For models with y > 0, the conditional distribution is often heteroskedastic or skewed, while ln( y ) is much less so The distribution of ln( y ) is more narrow, limiting the effect of outliers
Economics 20 - Prof. Anderson

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ 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