LinearRegression4

866137 0004491 guard 2309324 2312244 0021537 forward

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Unformatted text preview: ***************************************** Variable Coefficient t-statistic t-probability intercept 4.759456 4.039552 0.000070 exper 1.218765 3.657574 0.000308 expersq -0.069043 -2.866137 0.004491 guard 2.309324 2.312244 0.021537 forward 1.586096 1.586106 0.113917 marr 0.559836 0.758389 0.448897 When marr is added to the regression, its coefficient is about .5598 (SE = 0.738). Therefore, a married player is estimated to score just over half a point more per game (experience and position held fixed), but the estimate is not statistically different from zero (p-value = .43). So, based on points per game, we cannot conclude married players are more productive. VER. 10/23/2012. © P. KOLM 25 (v) Add interactions of marital status with both experience variables. In this expanded model, is there strong evidence that marital status affects points per game? Solution: Adding interactions of marital status with both experience variables, the new estimated regression equation becomes points = 5.892 + 0.6845exper − 0.02838exper 2 + 2.271guard (1.34) (0.433) (0.0326) (1.00) 1.677 forward − 2.624marr + 1.292marr ⋅ exper − 0.09360marr ⋅ exper 2 (1.00) (2.03) (0.680) n = 269, R2 = 0.106, VER. 10/23/2012. © P. KOLM (0.0487) R2 = 0.082 26 Ordinary Least-squares Estimates Dependent Variable = points R-squared = 0.1058 Rbar-squared = 0.0818 sigma^2 = 31.7724 Durbin-Watson = 2.1971 Nobs, Nvars = 269, 8 *************************************************************** Variable Coefficient t-statistic t-probability intercept 5.892488 4.382200 0.000017 exper 0.684538 1.581960 0.114870 expersq -0.028377 -0.871246 0.384421 guard 2.270909 2.277849 0.023544 forward 1.677190 1.679017 0.094346 marr -2.623669 -1.291201 0.197776 marrexp 1.291512 1.898735 0.058702 marrexpsq -0.093597 -1.921103 0.055808 We compare this new model with the restricted model in part (i) and found the F statistic and p-value shown below. We conclude that there is not very strong evidence that marital status has any partial effect on points scored. F statistic p value VER. 10/23/2012. © P. KOLM = = 1.4439 0.2304 27 (vi) Estimate the model from part (iv) but use assists per game as the dependent variable. Are there any notable differences from part (iv)? Discuss. Solution: Using assists per game as the dependent variable, the new estimated regression equation and output are assists = −0.3318 + 0.4814exper − 0.02951exper 2 (0.365) (0.103) (0.00746) 2.551guard + 0.5145 forward + 0.3453marr (0.309) (0.310) n = 269, R2 = 0.348, VER. 10/23/2012. © P. KOLM (0.229) R2 = 0.336 28 Ordinary Least-squares Estimates Dependent Variable = assists R-squared = 0.3479 Rbar-squared = 0.3355 sigma^2 = 3.0665 Durbin-Watson = 2.1470 Nobs, Nvars = 269, 6 *************************************************************** Variable Coefficient t-statistic t-probability intercept -0.331770 -0.909413 0.363965 exper 0.481352 4.665340 0.000005 expersq -0.029514 -3.956940 0.000098 guard 2.550615 8.247859 0.000000 forward 0.514483 1.661583 0.097788 marr 0.345333 1.510835 0.132031 From the output above, we c...
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This document was uploaded on 02/17/2014 for the course COURANT G63.2751.0 at NYU.

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