Call: lm(formula = wage ~ age + agesq + exper, data = nbasal) Residuals: Min 1Q
ID: 3223126 • Letter: C
Question
Call:
lm(formula = wage ~ age + agesq + exper, data = nbasal)
Residuals:
Min 1Q Median 3Q Max
-2268.8 -608.0 -173.0 378.3 4478.5
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 65.505 2985.866 0.022 0.983
age 123.113 206.307 0.597 0.551
agesq -4.202 3.614 -1.163 0.246
exper 231.988 48.705 4.763 0.00000314 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 906.3 on 265 degrees of freedom
Multiple R-squared: 0.1875, Adjusted R-squared: 0.1783
F-statistic: 20.39 on 3 and 265 DF, p-value: 0.000000000006448
> summary(mod2)
Call:
lm(formula = lwage ~ age + agesq + exper, data = nbasal)
Residuals:
Min 1Q Median 3Q Max
-2.4771 -0.3900 0.1087 0.4969 1.8959
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.24357 2.58563 1.641 0.1019
age 0.24852 0.17865 1.391 0.1654
agesq -0.00710 0.00313 -2.269 0.0241 *
exper 0.25593 0.04218 6.068 0.00000000446 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.7848 on 265 degrees of freedom
Multiple R-squared: 0.216, Adjusted R-squared: 0.2072
F-statistic: 24.34 on 3 and 265 DF, p-value: 0.00000000000006049
> mod1<-lm(wage~age+agesq+exper,data=nbasal)
> mod2<-lm(lwage~age+agesq+exper,data=nbasal)
> mod3<-lm(lwage~age+agesq+exper+draft+experXdraft,data=nbasal)
> mod4<-lm(lwage~age+agesq+draft,data=nbasal)
> mod5<-lm(lwage~age+agesq+exper+draft,data=nbasal)
> mod6<-lm(lwage~age+agesq+exper+draft+exper_10Xdraft,data=nbasal)
> mod7<-lm(lwage~age_30+agesq_30+exper_10+draft_1+exper_10Xdraft_1,data=nbasal)
>
>
> summary(mod1)
Call:
lm(formula = wage ~ age + agesq + exper, data = nbasal)
Residuals:
Min 1Q Median 3Q Max
-2268.8 -608.0 -173.0 378.3 4478.5
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 65.505 2985.866 0.022 0.983
age 123.113 206.307 0.597 0.551
agesq -4.202 3.614 -1.163 0.246
exper 231.988 48.705 4.763 0.00000314 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 906.3 on 265 degrees of freedom
Multiple R-squared: 0.1875, Adjusted R-squared: 0.1783
F-statistic: 20.39 on 3 and 265 DF, p-value: 0.000000000006448
> summary(mod2)
Call:
lm(formula = lwage ~ age + agesq + exper, data = nbasal)
Residuals:
Min 1Q Median 3Q Max
-2.4771 -0.3900 0.1087 0.4969 1.8959
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.24357 2.58563 1.641 0.1019
age 0.24852 0.17865 1.391 0.1654
agesq -0.00710 0.00313 -2.269 0.0241 *
exper 0.25593 0.04218 6.068 0.00000000446 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.7848 on 265 degrees of freedom
Multiple R-squared: 0.216, Adjusted R-squared: 0.2072
F-statistic: 24.34 on 3 and 265 DF, p-value: 0.00000000000006049
> summary(mod3)
Call:
lm(formula = lwage ~ age + agesq + exper + draft + experXdraft,
data = nbasal)
Residuals:
Min 1Q Median 3Q Max
-2.44617 -0.32023 0.04864 0.34504 1.65358
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.2289561 2.0142509 0.610 0.54237
age 0.4420529 0.1387197 3.187 0.00164 **
agesq -0.0072206 0.0024120 -2.994 0.00305 **
exper -0.0409674 0.0401862 -1.019 0.30905
draft -0.0559423 0.0048970 -11.424 < 0.0000000000000002 ***
experXdraft 0.0053594 0.0006204 8.638 0.000000000000000904 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.587 on 234 degrees of freedom
(29 observations deleted due to missingness)
Multiple R-squared: 0.4854, Adjusted R-squared: 0.4744
F-statistic: 44.14 on 5 and 234 DF, p-value: < 0.00000000000000022
> summary(mod4)
Call:
lm(formula = lwage ~ age + agesq + draft, data = nbasal)
Residuals:
Min 1Q Median 3Q Max
-2.49422 -0.30751 0.09283 0.41890 2.63707
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.079132 2.276060 -0.035 0.97229
age 0.458965 0.160309 2.863 0.00457 **
agesq -0.006601 0.002787 -2.369 0.01866 *
draft -0.019653 0.002387 -8.232 0.0000000000000126 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.6836 on 236 degrees of freedom
(29 observations deleted due to missingness)
Multiple R-squared: 0.296, Adjusted R-squared: 0.2871
F-statistic: 33.08 on 3 and 236 DF, p-value: < 0.00000000000000022
> summary(mod5)
Call:
lm(formula = lwage ~ age + agesq + exper + draft, data = nbasal)
Residuals:
Min 1Q Median 3Q Max
-2.48241 -0.32755 0.07521 0.40247 2.36712
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.567791 2.307837 0.679 0.49760
age 0.402755 0.158883 2.535 0.01190 *
agesq -0.007615 0.002764 -2.755 0.00632 **
exper 0.120535 0.040764 2.957 0.00342 **
draft -0.017814 0.002430 -7.330 0.00000000000368 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.6727 on 235 degrees of freedom
(29 observations deleted due to missingness)
Multiple R-squared: 0.3213, Adjusted R-squared: 0.3097
F-statistic: 27.81 on 4 and 235 DF, p-value: < 0.00000000000000022
> summary(mod6)
Call:
lm(formula = lwage ~ age + agesq + exper + draft + exper_10Xdraft,
data = nbasal)
Residuals:
Min 1Q Median 3Q Max
-2.44617 -0.32023 0.04864 0.34504 1.65358
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.2289561 2.0142509 0.610 0.54237
age 0.4420529 0.1387197 3.187 0.00164 **
agesq -0.0072206 0.0024120 -2.994 0.00305 **
exper -0.0409674 0.0401862 -1.019 0.30905
draft -0.0023482 0.0027754 -0.846 0.39836
exper_10Xdraft 0.0053594 0.0006204 8.638 0.000000000000000904 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.587 on 234 degrees of freedom
(29 observations deleted due to missingness)
Multiple R-squared: 0.4854, Adjusted R-squared: 0.4744
F-statistic: 44.14 on 5 and 234 DF, p-value: < 0.00000000000000022
> summary(mod7)
Call:
lm(formula = lwage ~ age_30 + agesq_30 + exper_10 + draft_1 +
exper_10Xdraft_1, data = nbasal)
Residuals:
Min 1Q Median 3Q Max
-2.43580 -0.33069 0.06267 0.34895 1.64246
Coefficients: (1 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.5386337 0.1023549 73.652 < 0.0000000000000002 ***
age_30 0.4327157 0.1381964 3.131 0.00196 **
agesq_30 -0.0071008 0.0024064 -2.951 0.00349 **
exper_10 -0.0395884 0.0395991 -1.000 0.31847
draft_1 NA NA NA NA
exper_10Xdraft_1 0.0056981 0.0004738 12.027 < 0.0000000000000002 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.5866 on 235 degrees of freedom
(29 observations deleted due to missingness)
Multiple R-squared: 0.4838, Adjusted R-squared: 0.475
F-statistic: 55.06 on 4 and 235 DF, p-value: < 0.00000000000000022
> anova(mod3,mod4)
Analysis of Variance Table
Model 1: lwage ~ age + agesq + exper + draft + experXdraft
Model 2: lwage ~ age + agesq + draft
Res.Df RSS Df Sum of Sq F Pr(>F)
1 234 80.623
2 236 110.287 -2 -29.664 43.048 < 0.00000000000000022 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> anova(mod3,mod5)
Analysis of Variance Table
Model 1: lwage ~ age + agesq + exper + draft + experXdraft
Model 2: lwage ~ age + agesq + exper + draft
Res.Df RSS Df Sum of Sq F Pr(>F)
1 234 80.623
2 235 106.331 -1 -25.708 74.614 0.000000000000000904 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
test the null hupothesis that ln(wage) is linear in the player's age. What is the p-value?
In wage) 30- 2agesq-t-B 3eaper B4draft+B5erper *draft-+EExplanation / Answer
Part-A
To test the null hypothesis that ln(wage) is linear in the players’ age we have to test that the coefficient of agesq=0
From suumary(mod3) we have p-value of test of coefficient of agesq is p=0.00305
As p-value is less than 0.05, we conclude that agesq is significant and hence ln(wage) is not linear in the players’ age.
Part-B
From mode 3 summary, we have F(5, 234)=44.14 with p< 0.00000000000000022
As p-value is less than 0.05, we reject the joint null hypothesis and conclude at least one coefficient is significantly different from zero.
Part-C
From anova(mod3,mod4) results we have F(2,236)43.048, p < 0.00000000000000022
As p-value is less than 0.05,, we reject the null hypothesis and conclude that experience affect ln(wage) significantly.
Part-D
From suumary(mod3) we have p-value of test of coefficient of interaction of experience and draft is p= 0.000000000000000904
As p-value is less than 0.05, we reject the null hypothesis and conclude that the interaction of experience and draft significantly affect ln(wage)
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