Consider the following wage equation: Where lnwi is individual i\'s log wage, ed
ID: 3358508 • Letter: C
Question
Consider the following wage equation: Where lnwi is individual i's log wage, edi; measures individual i's years of completed education, and expi measures individual s ears o experience and emalei Is a dummv variable Indicatlng whether individual 18 a female. is an unobserved error term. The R2-0.283. You estimate regression (1) on a sample of male and female workers in the their 30s and living and working in the UK. The sample size is 453. You obtain the following estimates: Coefficient Estimate Standard error 30 31 32 3 34 0.0473 0.0818 0.0721 0.00207 -0.155 0.0112 0.0052 0.0074 0.000293 0.0521Explanation / Answer
Question-1)
Interpret the R2 and Test over all significance of model:
Answer) R2 is a Coefficient of determination and is a statistical measure of how close the data are to the fitted regression line. In the given regression-1 R2 is low and got increased to 0.293 from 0.283. Since there is improvement in the R-squared because of addition of Test variable (Achievement Score) Model 2 and 3 combined able to capture extra information. Also the standard errors of beta1 and Gamma1 are less than 0.05 in model 2 and 3 we can conclude that both the values are significant enough to consider in the regression. Also there should be considered similar variable to capture corelations to increase R-squared for covering more information from DATA.
Question-2)
Compare the standard error of Beta1 in model 2 and model 1 and explain possible reasons for this change.
Answer)
In Beta1 of Model 1 the standard error is 0.0052 where as for Model 2 is 0.0032.
In Model-1 the beta1 is not significant enough to explain data in the regression since it is more than 0.005.
Where are in Model-2 Beta1 is less than threshold significant level and able to explain better in model-2 than in model-1
Question-3)
Under which assumptions can you interpret the coefficient Beta1 as the causal effect of education on wages?
Answer)
Assumption of predictions must be within +/- 5% of the actual value which can be interpreted from the standard error.
In the Model-1 we got less standard error but not significant with respect to our assumption.
And due to causal effect of educaiton on wages standard error became less and significant to explain the data in model-2 which is less than
our assumption value 0.05.
Question-4)
Is the information provided about the estimates of regressions 2 and 3 sufficient for you to explain why the coefficient on
education is different between regression 1 and regression 2.
Answer)
No I dont think the information provided about the estimates are sufficient.It also depends on Rsquared and it might be increased
or decreased in capturing the data through regression. Also standard error is also a factor to consider for statistical significance.
Question-5)
Is either one of the log wage regressions likely to provide a good indication of the causal effect of education on wages?
Answer) Yes its true. Regression 2 and 3 likely to provide a good indication of causal effect of education on wages by observing
and increase in Rsquared value with significant coefficients.
Question-6)
Answer) Rsquared is 0.360(Model-4) from 0.283 (Model-1). There is an increase of Rsquared value which indicates the siginificance
and improvement in capturing the data by adding varaible Tenure in Model-4. Also Tenure newly added variable made the model to capture hidden pattern in the
from the data and hence more Rsquared value.
The hypotheses for the F-test of the overall significance can be done using
Null hypothesis: (Rsquared of model 4 - Rsquaredof model 1)>0
Alternative hypothesis: Difference is less than or equal to zero.
From F-test we can conclude the F value is greater than threshold value and cant reject null hypothesis. So Model -4 improved compared to Model-1 by adding additional
variables in model -4.