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Variable
Coefficient
tstatistic
tprobability
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 (pvalue = .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 Leastsquares Estimates
Dependent Variable =
points
Rsquared
=
0.1058
Rbarsquared
=
0.0818
sigma^2
=
31.7724
DurbinWatson =
2.1971
Nobs, Nvars
=
269,
8
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Variable
Coefficient
tstatistic
tprobability
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 pvalue 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 Leastsquares Estimates
Dependent Variable =
assists
Rsquared
=
0.3479
Rbarsquared
=
0.3355
sigma^2
=
3.0665
DurbinWatson =
2.1470
Nobs, Nvars
=
269,
6
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Variable
Coefficient
tstatistic
tprobability
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.
 Fall '14

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