solution:
Given data:
18.
The regression line is:
, thus for a male worker with 12 years of schooling, the predicted value of the log of hourly wage is:
19.
Here we are testing the hypothesis that:
. To the test the above hypothesis the test statistic is given by:
, which follows a t distribution with n-2= 21-2 = 19 degrees of freedom. Thus the test statistic is:
. The critical value at a significance level 0.05 is given by: . Here test statistic lies beyond the critical value thus we reject the null hypothesis. i.e. there is enough evidence to support the claim that .
20)
we need to find the 95% Confidence interval for ttge population parameter
And the confidence interval is given by:
where is the critical value of t distribution with n-2 df and at level of significance.
n = sample size
= 0.0736
= 0.016
n = 21
= 2.093024
It is calculated in R
code is attahced herewith.
> at (0.975, 19)
[1] 2 .093024
So 95% CI is given by:
(0.04011162, 0.1070884)
As we can aslo verify this from the above given output.
21)
Here we need to find the Total Sum of Squares
As we know that
where
TSS = Total sum of squares
SSR = Sum of squares due to regression
SSE = Sum of squares due to Error
and we also know that
and
Similary we are also given with R - square = 0.525
and we know that
So TSS = 7.412
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Consider the relationship between hourly wage rate and education attainment. A random sample of 21 male...
Considering the following economic model of wages and education: wage-b0+b1educ+u, where wage is the individuals hourly wage, educ is the individual's years of schooling, u is the error and b0 and b1 are population parameters Do you expect b1 to be positive or negative. Explain your answer. [2 points] Explain intuitively how an OLS regression fits the relationship between wage and education. [3 points) ii. Showing all of your working, derive the OLS estimators of b0 and b1. [6 points]
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