The classical errors-in-variables (CEV) assumption is that the measurement error has zero mean and is uncorrelated with the unobserved explanatory variable:
Cov(tvhours*, e) = 0 and mean(e) = 0
With tvhour = tvhours* + eCEV is not likely to hold because it is likely to have relationship between error and motheduc/fatheduc. It is because higher education of parents will lead to less time being with their children, resulting in underreport tvhours*.
data_c2 <- wage2
model_1 <- lm(log(wage)~ educ+ exper+tenure+married+ south+urban+black, data= data_c2)
model_2 <- lm(log(wage)~ educ+ exper+tenure+married+ south+urban+black+KWW, data= data_c2)
summary(model_1)##
## Call:
## lm(formula = log(wage) ~ educ + exper + tenure + married + south +
## urban + black, data = data_c2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.98069 -0.21996 0.00707 0.24288 1.22822
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.395497 0.113225 47.653 < 2e-16 ***
## educ 0.065431 0.006250 10.468 < 2e-16 ***
## exper 0.014043 0.003185 4.409 1.16e-05 ***
## tenure 0.011747 0.002453 4.789 1.95e-06 ***
## married 0.199417 0.039050 5.107 3.98e-07 ***
## south -0.090904 0.026249 -3.463 0.000558 ***
## urban 0.183912 0.026958 6.822 1.62e-11 ***
## black -0.188350 0.037667 -5.000 6.84e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3655 on 927 degrees of freedom
## Multiple R-squared: 0.2526, Adjusted R-squared: 0.2469
## F-statistic: 44.75 on 7 and 927 DF, p-value: < 2.2e-16summary(model_2)##
## Call:
## lm(formula = log(wage) ~ educ + exper + tenure + married + south +
## urban + black + KWW, data = data_c2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.04494 -0.21931 -0.00048 0.24163 1.26464
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.358797 0.113600 47.172 < 2e-16 ***
## educ 0.057628 0.006838 8.428 < 2e-16 ***
## exper 0.012228 0.003241 3.773 0.000172 ***
## tenure 0.011072 0.002456 4.507 7.40e-06 ***
## married 0.189461 0.039077 4.848 1.46e-06 ***
## south -0.091601 0.026156 -3.502 0.000484 ***
## urban 0.175545 0.027032 6.494 1.36e-10 ***
## black -0.164267 0.038530 -4.263 2.22e-05 ***
## KWW 0.005028 0.001819 2.764 0.005820 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3642 on 926 degrees of freedom
## Multiple R-squared: 0.2587, Adjusted R-squared: 0.2523
## F-statistic: 40.39 on 8 and 926 DF, p-value: < 2.2e-16model_1 <- lm(log(wage)~ educ+ exper+tenure+married+ south+urban+black, data= data_c2)
model_3 <- lm(log(wage)~ educ+ exper+tenure+married+ south+urban+black+KWW+IQ, data= data_c2)
summary(model_1)##
## Call:
## lm(formula = log(wage) ~ educ + exper + tenure + married + south +
## urban + black, data = data_c2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.98069 -0.21996 0.00707 0.24288 1.22822
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.395497 0.113225 47.653 < 2e-16 ***
## educ 0.065431 0.006250 10.468 < 2e-16 ***
## exper 0.014043 0.003185 4.409 1.16e-05 ***
## tenure 0.011747 0.002453 4.789 1.95e-06 ***
## married 0.199417 0.039050 5.107 3.98e-07 ***
## south -0.090904 0.026249 -3.463 0.000558 ***
## urban 0.183912 0.026958 6.822 1.62e-11 ***
## black -0.188350 0.037667 -5.000 6.84e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3655 on 927 degrees of freedom
## Multiple R-squared: 0.2526, Adjusted R-squared: 0.2469
## F-statistic: 44.75 on 7 and 927 DF, p-value: < 2.2e-16summary(model_3)##
## Call:
## lm(formula = log(wage) ~ educ + exper + tenure + married + south +
## urban + black + KWW + IQ, data = data_c2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.05704 -0.21621 0.00824 0.23725 1.24895
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.175644 0.127776 40.506 < 2e-16 ***
## educ 0.049837 0.007262 6.863 1.24e-11 ***
## exper 0.012752 0.003231 3.947 8.51e-05 ***
## tenure 0.010925 0.002446 4.467 8.92e-06 ***
## married 0.192145 0.038909 4.938 9.35e-07 ***
## south -0.082029 0.026222 -3.128 0.00181 **
## urban 0.175823 0.026910 6.534 1.06e-10 ***
## black -0.130399 0.039901 -3.268 0.00112 **
## KWW 0.003826 0.001852 2.066 0.03913 *
## IQ 0.003118 0.001013 3.079 0.00214 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3625 on 925 degrees of freedom
## Multiple R-squared: 0.2662, Adjusted R-squared: 0.2591
## F-statistic: 37.28 on 9 and 925 DF, p-value: < 2.2e-16In part ii, KWW and IQ are independently significant at 5%.
((0.2662-0.2526)/2)/((1-0.2662)/925)## [1] 8.571818Based on F-test =8.57 >1 -> The two variables are jointly significant.
data_c8 <- twoyear
mean <- mean(data_c8$stotal)
sd <- sd(data_c8$stotal)
mean## [1] 0.04748291sd## [1] 0.8535441model_1 <- lm(stotal ~ jc+ univ, data= data_c8)
summary(model_1)##
## Call:
## lm(formula = stotal ~ jc + univ, data = data_c8)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.0298 -0.4457 0.1220 0.4522 2.4846
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.295005 0.013196 -22.356 < 2e-16 ***
## jc 0.074767 0.012170 6.143 8.53e-10 ***
## univ 0.164644 0.004091 40.246 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7667 on 6760 degrees of freedom
## Multiple R-squared: 0.1934, Adjusted R-squared: 0.1932
## F-statistic: 810.5 on 2 and 6760 DF, p-value: < 2.2e-16problems in the dataset
problems in the dataset
v.problems in the dataset