Christopher Dougherty EC220 - Introduction to econometrics (chapter 1) Slideshow: exercise 1.16 Original citation: Dougherty, C. (2012) EC220 - Introduction to econometrics (chapter 1). [Teaching Resource] © 2012 The Author This version available at: 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

1.16 The output below shows the result of regressing weight in 2002 on height, using EAEF Data Set 21. In 2002 the respondents were aged 37–44. Explain why R 2 is lower than in the regression reported in Exercise reg WEIGHT02 HEIGHT Source | SS df MS Number of obs = F( 1, 538) = Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = WEIGHT02 | Coef. Std. Err. t P>|t| [95% Conf. Interval] HEIGHT | _cons | EXERCISE

2 The regression output above gives the result of regressing weight, measured in pounds, on height, measured in inches, using EAEF Data Set 21.. reg WEIGHT85 HEIGHT Source | SS df MS Number of obs = F( 1, 538) = Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = WEIGHT85 | Coef. Std. Err. t P>|t| [95% Conf. Interval] HEIGHT | _cons | reg WEIGHT02 HEIGHT Source | SS df MS Number of obs = F( 1, 538) = Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = WEIGHT02 | Coef. Std. Err. t P>|t| [95% Conf. Interval] HEIGHT | _cons |

3 EXERCISE 1.16 The first regression uses weight measured in 1985, when the respondents were aged 20 to 27. The second uses weight measured 17 years later in reg WEIGHT85 HEIGHT Source | SS df MS Number of obs = F( 1, 538) = Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = WEIGHT85 | Coef. Std. Err. t P>|t| [95% Conf. Interval] HEIGHT | _cons | reg WEIGHT02 HEIGHT Source | SS df MS Number of obs = F( 1, 538) = Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = WEIGHT02 | Coef. Std. Err. t P>|t| [95% Conf. Interval] HEIGHT | _cons |

. reg WEIGHT85 HEIGHT Source | SS df MS Number of obs = F( 1, 538) = Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = WEIGHT85 | Coef. Std. Err. t P>|t| [95% Conf. Interval] HEIGHT | _cons | reg WEIGHT02 HEIGHT Source | SS df MS Number of obs = F( 1, 538) = Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = WEIGHT02 | Coef. Std. Err. t P>|t| [95% Conf. Interval] HEIGHT | _cons | EXERCISE 1.16 The explained sum of squares (called by Stata the model sum of squares) is actually higher for 2002 than for So why is R 2 considerably lower in the second regression? (The next slide gives the answer, so think about it first.)

5 EXERCISE 1.16 As people age, they tend to put on weight. For this sample, mean weight was 157 pounds in 1985, and 184 pounds in reg WEIGHT85 HEIGHT Source | SS df MS Number of obs = F( 1, 538) = Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = WEIGHT85 | Coef. Std. Err. t P>|t| [95% Conf. Interval] HEIGHT | _cons | reg WEIGHT02 HEIGHT Source | SS df MS Number of obs = F( 1, 538) = Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = WEIGHT02 | Coef. Std. Err. t P>|t| [95% Conf. Interval] HEIGHT | _cons |

6 EXERCISE 1.16 Some people are more successful in resisting this tendency than others, either because of their genetic make-up or because they have a healthier life-style.. reg WEIGHT85 HEIGHT Source | SS df MS Number of obs = F( 1, 538) = Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = WEIGHT85 | Coef. Std. Err. t P>|t| [95% Conf. Interval] HEIGHT | _cons | reg WEIGHT02 HEIGHT Source | SS df MS Number of obs = F( 1, 538) = Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = WEIGHT02 | Coef. Std. Err. t P>|t| [95% Conf. Interval] HEIGHT | _cons |

7 EXERCISE 1.16 Thus the variance in weight also tends to increase. You can see that there has been a huge increase in the total sum of squares.. reg WEIGHT85 HEIGHT Source | SS df MS Number of obs = F( 1, 538) = Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = WEIGHT85 | Coef. Std. Err. t P>|t| [95% Conf. Interval] HEIGHT | _cons | reg WEIGHT02 HEIGHT Source | SS df MS Number of obs = F( 1, 538) = Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = WEIGHT02 | Coef. Std. Err. t P>|t| [95% Conf. Interval] HEIGHT | _cons |

8 EXERCISE 1.16 Consequently, although the explained sum of squares accounted for by height has increased, it has become a smaller proportion of the total sum of squares and R 2 has fallen.. reg WEIGHT85 HEIGHT Source | SS df MS Number of obs = F( 1, 538) = Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = WEIGHT85 | Coef. Std. Err. t P>|t| [95% Conf. Interval] HEIGHT | _cons | reg WEIGHT02 HEIGHT Source | SS df MS Number of obs = F( 1, 538) = Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = WEIGHT02 | Coef. Std. Err. t P>|t| [95% Conf. Interval] HEIGHT | _cons |

Copyright Christopher Dougherty 1999–2006. This slideshow may be freely copied for personal use