Interpret the coefficient on in the second regression in a sentence. (The meaning INJURED is different in the two regressions). Explain why the coefficient is different than INJURED in the first regression. Holding age constant, players that were injured in the previous season are expected to have an average WS48 that’s .0224 relative to players that were not injured. The coefficients are different because, in the simple first regression, INJURED picked up the effect of the confounding factor Age. WS48 = .1203 - .03254 INJURED (66.37) (-6.34) WS48 = .1992 - .0274 INJURED - .00279 Age (18.38) (-5.41) (-7.37) t-statistics in parentheses There are two 25 year old basketball players with similar abilities. One was injured last season, one wasn’t. On average, how different will their WS48’s be next year? We are comparing two people of the same Age, and asking about the impact of an injury (INJURED). Therefore, we need to use the second regression that holds Age constant. The one who is injured will on average have a - .0274 WS48 Hard, intuition and thought (or luck): Based on the difference between the coefficient on in the simple regression and the multivariate regression, do you think that injured INJURED players are older or younger than non-injured players, on average? Note: Older people (Age) have lower WS48. In both equations, INJURED decreases WS48. Without controlling for Age, the impact of INJURED was a larger negative. So it must be that the people who were injured were causing the impact of INJURED to pick up this confounding age factor. There are three basketball positions forward, guard and center. I therefore make two new – dummy variables, and I run this regression: Forward Guard. = .2152 - .0289 - .00284 - .01194 -.02485 WS48 INJURED Age Forward Guard (18.80) (-5.79) (-7.58) (-2.69) (-5.58) t-statistics in parentheses e. Holding and constant, what is the difference in between and Age INJURED WS48 Forwards CIRCLE AND FILL IN BLANK Centers? is the excluded (reference) category! Centers have LOWER than Forwards WS48 Centers.
Interpret the coefficient on INJURED in the second regression in a sentence. (The meaning is different in the two regressions). Explain why the INJURED coefficient is different than in the first regression. Holding age constant, players that were injured in the previous season are expected to have an average WS48 that’s .0224 relative to players that were not injured. The coefficients are different because, in the simple first regression, INJURED picked up the effect of the confounding factor Age. WS48 = .1203 - .03254 INJURED (66.37) (-6.34) WS48 = .1992 - .0274 INJURED - .00279 Age (18.38) (-5.41) (-7.37) t-statistics in parentheses There are two 25 year old basketball players with similar abilities. One was injured last season, one wasn’t. On average, how different will their WS48’s be next year? We are comparing two people of the same Age, and asking about the impact of an injury (INJURED). Therefore, we need to use the second regression that holds Age constant. The one who is injured will on average have a - .0274 WS48 Hard, intuition and thought (or luck): Based on the difference between the coefficient on INJURED in the simple regression and the multivariate regression, do you think that injured players are older or younger than non-injured players, on average? Note: Older people (Age) have lower WS48. In both equations, INJURED decreases WS48. Without controlling for Age, the impact of INJURED was a larger negative. So it must be that the people who were injured were causing the impact of INJURED to pick up this confounding age factor. There are three basketball positions – forward, guard and center. I therefore make two new dummy variables, Forward and Guard. I run this regression: WS48 = .2152 - .0289 INJURED - .00284 Age - .01194 Forward -.02485 Guard (18.80) (-5.79) (-7.58) (-2.69) (-5.58) t-statistics in parentheses e. Holding Age and INJURED constant, what is the difference in WS48 between Forwards and Centers? CIRCLE AND FILL IN BLANK Centers is the excluded (reference) category! Forwards have LOWER WS48 than Centers.
InClass-Exercises-Solutions.docx