Question 1: Wage and education Use the STATA output at the end of this handout t
ID: 3314428 • Letter: Q
Question
Question 1: Wage and education
Use the STATA output at the end of this handout to answer the following questions:
Model 1
a) Interpret the regression coefficients (both slope and the intercept) in model 1.
b) Write down the predicted model. How much would you expect someone to make if they have 10 years of education?
c) If someone in your sample has 10 years of education and has a wage = 5, what does their residual equal? Give me one possible reason why a person might have such a residual.
d) Is the slope coefficient in model 1 statistically significant at the 5 percent level? Explain using the p-value. (For this problem, you do NOT have to spell out the distribution of the test statistic, etc.) Also be explicit about what we are actually testing- in both the language of hypothesis testing and in everyday English.
e) What is the formula for ˆ1? Based on the available information, what is the variance of education? What is the covariance between education and wages?
f) Given the answer in e, find the correlation between education and wages. Then, square it. What does it equal (find the value that it equals to in the STATA output)? (give both the value it is equal to and the name of what it equals)
g) Give two formulas for the coefficient of determination. Explain the intuitive meaning of each and then show with values from STATA output that the do indeed give you the correct R-squared value.
desc wage educ exper storage display value label variable name type format variable label wage educ exper float %9.0g byte %8.0g byte %8.0g hourly wage years of schooling years of workforce experience . sum wage educ exper Variable Obs Mean Std. Dev. Min Max wage educ exper I 1260 1260 1260 6.30669 12.56349 18.20635 1.02 4.660639 2.624489 11.96349 77.72 17 48 REGRESSION MODEL 1: .eg Wage eauc 1260 E1, 1258)-59.40 0.0000 = 0.0451 di R-squared0.0443 4.5562 Source df MS Number of obs Model 1232.965481 1232.96548 26114.4737 1258 20.7587231 Prob F R-squared Residual Total 27347.4392 1259 21.7215561 Root MSE Wage l Coef. Std. Err. (95% Conf. Interval] educ cons l 3770664 1.56942 0489263 6279439 7.71 0.000 2.50 0.013 .2810802 3374873 .4730526 2.801353Explanation / Answer
We are allowed to do 4 subparts question at a time. Post again for more subparts of question.
a) Interpret the regression coefficients (both slope and the intercept) in model 1.
Ans: Slope: It says that for every 1 unit increase in education, wage increases by 0.3770664 units.
Intercept: When a person has no education, wage = 1.56942 units.
b) Write down the predicted model. How much would you expect someone to make if they have 10 years of education?
Ans: y = 1.56942 + 0.3770664 * x
when x = 10
y = 1.56942 + 0.3770664 * 10
Wage = 5.340084
c) If someone in your sample has 10 years of education and has a wage = 5, what does their residual equal? Give me one possible reason why a person might have such a residual.
Ans: Residual = 5 - 5.340084 = - 0.340084
Because, model is not a perfect 100% fit, that's why residual
d) Is the slope coefficient in model 1 statistically significant at the 5 percent level? Explain using the p-value. (For this problem, you do NOT have to spell out the distribution of the test statistic, etc.) Also be explicit about what we are actually testing- in both the language of hypothesis testing and in everyday English.
Ans:
p value = 0 < 0.05
Null is rejected
Slope is thus significant.
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