Problem SET 1 (25 points): Using data from GSS 1998 (sample size = 1,841), A researcher is examining how much education and occupational prestige affect individual income. Education is measured in years (range: 0 through 20) and occupational prestige from 17 to 86. Household income is measured in thousand-dollar increments (1 indicates 1,000 dollars) and ranges from 0.75 (=$750) to 125 (=$125,000). She generates the following statistics (Table 1):

Table 1: correlation, mean, and standard deviation (SD).

Education Occupational prestige

Education 1.00

Occupational .51 1.00 prestige

Individual income .36 .38

Individual income

1.00

Mean SD

13.8 2.7 44.6 13.6

29.9 24.2

She also implemented a regression model using STATA. In the STATA regression readout below, estimated slopes of education (educ) and occupational prestige (prestg80) and for the intercept (_cons) have been removed.

1

a) Using information in Table 1 (correlations, mean, and SD), compute slopes for education and occupational prestige and the intercept. Write out the multiple regression equation for these data. Show your work for how you computed the intercept and the slopes.

• Compute the slope for education (2 points)
• Compute the slope for occupational prestige (2 points)
• Compute the intercept (2 points)
• Write down multiple regression equation (2 points)
• Interpret the Intercept (2 points)
• Interpret the slope for education (2 points)
• Interpret the slope for occupational prestige (2 points)

2

b) Calculate the standardized betas for education and occupational prestige and report the results as a standardized regression equation. Interpret the two effects in terms of strength and direction. Show your work.

• Calculate the standard beta for education (2 points):
• Calculate the standard Beta for occupational prestige (2 points):
• Interpret the two effects in terms of strength and direction (3 points):

c) For the slope (coef.) of education, what range of values can we be 95% certain exists in the population? (critical value oftfor 95% = 1.96) That is, calculate and report the 95% CI of the slope of education. Show your work. (4 points)