The given equation assumes a linear relationship between the true weekly hours of television viewing (\(thours\)) and the child’s age, mother’s education, father’s education, and number of siblings.
This assumption requires that the errors in the reported hours of television viewing (\(vhours\)) are independent of the true values of weekly hours (\(thours\)).
Homoscedasticity implies that the variance of the errors in reported hours (\(vhours\)) is constant across different levels of true hours (\(thours\)).
Exogeneity assumes that the errors in reported hours (\(vhours\)) are uncorrelated with the true values of weekly hours (\(thours\)).
Now, let’s discuss whether we think the CEV assumptions are likely to hold in this application.
Linearity: Discuss whether a linear relationship is reasonable in the context of the study.
Independence: Consider factors that might influence independence, such as survey design and data collection methods.
Homoscedasticity: Assess whether the variance of reported hours is likely to be consistent across different levels of true hours.
Exogeneity: Discuss potential sources of correlation between errors in reporting and true values.
##
## Call:
## lm(formula = wage ~ educ + KWW, data = wage2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -906.43 -245.00 -34.28 197.40 2298.61
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -71.091 81.574 -0.871 0.384
## educ 43.460 6.019 7.221 1.07e-12 ***
## KWW 12.413 1.731 7.172 1.51e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 372.4 on 932 degrees of freedom
## Multiple R-squared: 0.1537, Adjusted R-squared: 0.1519
## F-statistic: 84.63 on 2 and 932 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = wage ~ educ + KWW + I(KWW^2), data = wage2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -953.39 -239.83 -30.71 201.54 2253.05
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 648.6825 207.7162 3.123 0.001846 **
## educ 42.0442 5.9887 7.021 4.26e-12 ***
## KWW -30.3570 11.4948 -2.641 0.008406 **
## I(KWW^2) 0.6198 0.1647 3.763 0.000178 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 369.8 on 931 degrees of freedom
## Multiple R-squared: 0.1664, Adjusted R-squared: 0.1637
## F-statistic: 61.94 on 3 and 931 DF, p-value: < 2.2e-16## Estimate Pr(>|t|)
## educ 42.0442036 4.255736e-12
## KWW -30.3569558 8.406367e-03
## I(KWW^2) 0.6198462 1.783083e-04## Loading required package: carData## Sample Mean of stotal: 0.04748291## Standard Deviation of stotal: 0.8535441##
## Call:
## lm(formula = jc ~ stotal, data = twoyear)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.3633 -0.3424 -0.3384 -0.3113 3.5196
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.338364 0.009403 35.983 <2e-16 ***
## stotal 0.011177 0.011001 1.016 0.31
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7721 on 6761 degrees of freedom
## Multiple R-squared: 0.0001527, Adjusted R-squared: 4.767e-06
## F-statistic: 1.032 on 1 and 6761 DF, p-value: 0.3097##
## Call:
## lm(formula = univ ~ stotal, data = twoyear)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4319 -1.8707 -0.4968 1.6909 7.8927
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.87073 0.02520 74.25 <2e-16 ***
## stotal 1.16968 0.02948 39.68 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.069 on 6761 degrees of freedom
## Multiple R-squared: 0.1889, Adjusted R-squared: 0.1888
## F-statistic: 1575 on 1 and 6761 DF, p-value: < 2.2e-16## Linear hypothesis test
##
## Hypothesis:
## jc - univ = 0
##
## Model 1: restricted model
## Model 2: lwage ~ stotal + jc + univ
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 6760 1417.9
## 2 6759 1417.8 1 0.16883 0.8049 0.3697## Linear hypothesis test
##
## Hypothesis:
## I(stotal^2) = 0
##
## Model 1: restricted model
## Model 2: lwage ~ stotal + I(stotal^2) + jc + univ
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 6759 1417.8
## 2 6758 1417.8 1 0.013251 0.0632 0.8016## Linear hypothesis test
##
## Hypothesis:
## stotal:jc = 0
## stotal:univ = 0
##
## Model 1: restricted model
## Model 2: lwage ~ stotal + jc + univ + stotal:jc + stotal:univ
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 6759 1417.8
## 2 6757 1417.5 2 0.28045 0.6684 0.5125