1. Christopher Dougherty EC220 - Introduction to econometrics (chapter 1) Slideshow: exercise 1.5 Original citation: Dougherty, C. (2012) EC220 - Introduction to econometrics (chapter 1). [Teaching Resource] © 2012 The Author This version available at: http://learningresources.lse.ac.uk/127/http://learningresources.lse.ac.uk/127/ Available in LSE Learning Resources Online: May 2012 This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 License. This license allows the user to remix, tweak, and build upon the work even for commercial purposes, as long as the user credits the author and licenses their new creations under the identical terms. http://creativecommons.org/licenses/by-sa/3.0/ http://creativecommons.org/licenses/by-sa/3.0/ http://learningresources.lse.ac.uk/

2. 1.5 The output below shows the result of regressing the weight of the respondent in 1985, measured in pounds, on his or her height, measured in inches. Provide an interpretation of the coefficients.. reg WEIGHT85 HEIGHT Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 1, 538) = 355.97 Model | 261111.383 1 261111.383 Prob > F = 0.0000 Residual | 394632.365 538 733.517407 R-squared = 0.3982 -------------+------------------------------ Adj R-squared = 0.3971 Total | 655743.748 539 1216.59322 Root MSE = 27.084 ------------------------------------------------------------------------------ WEIGHT85 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- HEIGHT | 5.192973.275238 18.87 0.000 4.6523 5.733646 _cons | -194.6815 18.6629 -10.43 0.000 -231.3426 -158.0204 ------------------------------------------------------------------------------ EXERCISE 1.5 1

3. . reg WEIGHT85 HEIGHT Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 1, 538) = 355.97 Model | 261111.383 1 261111.383 Prob > F = 0.0000 Residual | 394632.365 538 733.517407 R-squared = 0.3982 -------------+------------------------------ Adj R-squared = 0.3971 Total | 655743.748 539 1216.59322 Root MSE = 27.084 ------------------------------------------------------------------------------ WEIGHT85 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- HEIGHT | 5.192973.275238 18.87 0.000 4.6523 5.733646 _cons | -194.6815 18.6629 -10.43 0.000 -231.3426 -158.0204 ------------------------------------------------------------------------------ EXERCISE 1.5 2 The regression output above gives the result of regressing weight, measured in pounds, in 1985 on height, measured in inches, using EAEF data set 21.

4. . reg WEIGHT85 HEIGHT Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 1, 538) = 355.97 Model | 261111.383 1 261111.383 Prob > F = 0.0000 Residual | 394632.365 538 733.517407 R-squared = 0.3982 -------------+------------------------------ Adj R-squared = 0.3971 Total | 655743.748 539 1216.59322 Root MSE = 27.084 ------------------------------------------------------------------------------ WEIGHT85 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- HEIGHT | 5.192973.275238 18.87 0.000 4.6523 5.733646 _cons | -194.6815 18.6629 -10.43 0.000 -231.3426 -158.0204 ------------------------------------------------------------------------------ EXERCISE 1.5 3 The coefficient of height is 5.19. This implies that a one-unit increase in height increases weight by 5.19 units.

5. . reg WEIGHT85 HEIGHT Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 1, 538) = 355.97 Model | 261111.383 1 261111.383 Prob > F = 0.0000 Residual | 394632.365 538 733.517407 R-squared = 0.3982 -------------+------------------------------ Adj R-squared = 0.3971 Total | 655743.748 539 1216.59322 Root MSE = 27.084 ------------------------------------------------------------------------------ WEIGHT85 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- HEIGHT | 5.192973.275238 18.87 0.000 4.6523 5.733646 _cons | -194.6815 18.6629 -10.43 0.000 -231.3426 -158.0204 ------------------------------------------------------------------------------ EXERCISE 1.5 4 The units of height are inches and those of weight are pounds. So the coefficient implies that weight increases by 5.19 pounds for each additional inch of height.

6. . reg WEIGHT85 HEIGHT Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 1, 538) = 355.97 Model | 261111.383 1 261111.383 Prob > F = 0.0000 Residual | 394632.365 538 733.517407 R-squared = 0.3982 -------------+------------------------------ Adj R-squared = 0.3971 Total | 655743.748 539 1216.59322 Root MSE = 27.084 ------------------------------------------------------------------------------ WEIGHT85 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- HEIGHT | 5.192973.275238 18.87 0.000 4.6523 5.733646 _cons | -194.6815 18.6629 -10.43 0.000 -231.3426 -158.0204 ------------------------------------------------------------------------------ EXERCISE 1.5 5 The intercept is –194.7. Literally it implies that a person with zero height weighs minus 195 pounds.

7. . reg WEIGHT85 HEIGHT Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 1, 538) = 355.97 Model | 261111.383 1 261111.383 Prob > F = 0.0000 Residual | 394632.365 538 733.517407 R-squared = 0.3982 -------------+------------------------------ Adj R-squared = 0.3971 Total | 655743.748 539 1216.59322 Root MSE = 27.084 ------------------------------------------------------------------------------ WEIGHT85 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- HEIGHT | 5.192973.275238 18.87 0.000 4.6523 5.733646 _cons | -194.6815 18.6629 -10.43 0.000 -231.3426 -158.0204 ------------------------------------------------------------------------------ EXERCISE 1.5 6 How can we explain this nonsense result? (Try to work it out yourself, before proceeding.)

8. . reg WEIGHT85 HEIGHT Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 1, 538) = 355.97 Model | 261111.383 1 261111.383 Prob > F = 0.0000 Residual | 394632.365 538 733.517407 R-squared = 0.3982 -------------+------------------------------ Adj R-squared = 0.3971 Total | 655743.748 539 1216.59322 Root MSE = 27.084 ------------------------------------------------------------------------------ WEIGHT85 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- HEIGHT | 5.192973.275238 18.87 0.000 4.6523 5.733646 _cons | -194.6815 18.6629 -10.43 0.000 -231.3426 -158.0204 ------------------------------------------------------------------------------ EXERCISE 1.5 7 One perfectly good explanation is that a height of zero makes no sense at all and the regression relationship has no meaning for such a value.

9. . reg WEIGHT85 HEIGHT Source | SS df MS Number of obs = 540 -------------+------------------------------ F( 1, 538) = 355.97 Model | 261111.383 1 261111.383 Prob > F = 0.0000 Residual | 394632.365 538 733.517407 R-squared = 0.3982 -------------+------------------------------ Adj R-squared = 0.3971 Total | 655743.748 539 1216.59322 Root MSE = 27.084 ------------------------------------------------------------------------------ WEIGHT85 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- HEIGHT | 5.192973.275238 18.87 0.000 4.6523 5.733646 _cons | -194.6815 18.6629 -10.43 0.000 -231.3426 -158.0204 ------------------------------------------------------------------------------ EXERCISE 1.5 8 Another explanation is that the true relationship is nonlinear, and the reason that we get a negative intercept is that the mathematical from of the relationship has been misspecified.

10. Copyright Christopher Dougherty 1999-2006. This slideshow may be freely copied for personal use. 18.06.06