Question

(d) Construct the t-statistic for the slope coefficient. Is this t-statistic significant at the 10% level? Clearly show your work including the critical value which you are using.
(e) Construct the t-statistic for the intercept coefficient. Is this t-statistic significant at the 1% level? Clearly show your work including the critical value which you are using.

1. [7 points] Suppose that a random sample of U.S. hired farmworkers is selected from the population of these workers and that these workers' average hours per week worked (hours) and ages (age) are recorded. (The data used for this problem come from the National Agricultural Workers Survey public-use file.) A regression of hours on age yields: R2 = 0.006, SER = 13.490 hours = 40.237 + 0.081age, (0.173) (0.005) (a) (i) Interpret the regression slope in words. Be sure to clearly indicate the economic magnitude of this result (i.e. a what size change in what variable translates into a what size change in what other variable?). (ii) Does the estimated regression intercept for this model have a relevant economic interpretation? Why or why not? Make sure to give a clear explanation. (b) (i) Interpret the R-squared goodness-of-fit statistic in words, making sure to indicate the magnitude. (ii)Interpret the standard error of the regression goodness-of-fit statistic in words, making sure to indicate the magnitude. (c) What is the regression's hours per week prediction for someone who is 20 years old? Show your work. (d) Construct the t-statistic for the slope coefficient. Is this t-statistic significant at the 10% level? Clearly show your work including the critical value which you are using. (e) Construct the t-statistic for the intercept coefficient. Is this t-statistic significant at the 1% level? Clearly show your work including the critical value which you are using. (1) Does least squares assumption 1 plausibly hold for this regression? Explain in detail why or why not. (g) Are the errors in this regression plausibly homoskedastic? Explain. (Hint: It may be helpful to think of economic "stories" about what might be happening in this context for older versus younger workers in order to relate your answer to the homoskedasticity definition.)

(f) Does least squares assumption 1 plausibly hold for this regression? Explain in detail why or why not.
(g) Are the errors in this regression plausibly homoskedastic? Explain. (Hint: It may be helpful to think of economic “stories” about what might be happening in this context for older versus younger workers in order to relate your answer to the homoskedasticity definition.)

Can you do the bottom 4, do not need help on 1,2 or 3

Answer 1

(a) (i) The slope of the regression equation is 0.081 which means that for every one year increase in the age, the average hours will increase by 0.081.

(ii) The estimated regression intercept makes no sense because, in the regression equation, age cannot be zero.

(b) (i) R-squared (R²) is a statistical measure that represents the proportion of the variance for average hours that's explained by age in a regression model.

(ii) The standard error of the estimate is a measure of the accuracy of predictions. The regression line is the line that minimizes the sum of squared deviations of prediction (also called the sum of squares error), and the standard error of the estimate is the square root of the average squared deviation.

(c) We have:

hours = 40.237 + 0.081*age

Put age = 20 years

hours = 40.237 + 0.081*20

hours = 41.857

(d) The hypothesis being tested is:

b₁ = 0

b₁ ≠ 0

t-statistic for the slope coefficient, t = b₁/ Standard error

= 0.081/13.490 = 0.006

The p-value is 0.5023.

Since the p-value (0.5023) is greater than the significance level, we cannot reject the null hypothesis.

Therefore, we cannot conclude that this t-statistic is significant at the 10% level.

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