SOC 201 Lab Section Week 13

Using a sample of Illinoisans, we want to know whether education is correlated with income. Data are presented below.

1. By hand, find the correlation, r, between education and income.

2. Does the correlation support the idea that higher education is associated with higher income?

3. Is the association observed in the sample statistically significant? What do we conclude from this test?

4. Calculate and interpret the meaning of the regression slope.

5. Calculate and interpret the meaning of the Y-intercept for the regression line.

6. Calculate and interpret the coefficient of determination.

7. Predict the income for an Illinoisan with 9 years of education.

8. Let's confirm our regression statistics in google sheets.

9.What's my grade?In Professor Krugman's economic course, the correlation between the students' total scores prior to the final examination and their final-examination scores is r = 0.5. The pre-exam totals for all students in the course have mean 280 and standard deviation 40. The final-exam scores have mean 75 and standard deviation 8. Professor Krugman has lost Julie's final exam but knows that her total before the exam was 300. He decides to predict her final-exam score from her pre-exam total.

(a) What is the slope of the least-squares regression line of final-exam scores on pre-exam total scores in this course? What is the intercept? Interpret the slope in the context of the problem.

(b) Use the regression line to predict Julie's score.

(c) Julie doesn't think this method accurately predicts how well she did on the final exam. Use r² to argue that her actual score could have been much higher (or much lower) than the predicted value.