Question

1. A researcher posits that height is associated with greater income among men. To test this, he records the height (in inches) and income (in thousands of dollars per year) in a random sample of 10 men. Compute Pearson correlation coefficient for the data listed in the following table.

X (Height)	Y (Income)
66	18
70	42
74	52
62	19
68	22
78	40
80	29
72	42
70	38
76	44

                          Pearson r             _______

2. Add 3 inches to the height of each male. What is the new correlation coefficient?

                          Pearson r             _______

3. Subtract $5,000 of income from each male. What is the new correlation coefficient?

                          Pearson r             _______

4. Divide the height of each male in half. What is the new correlation coefficient?

                          Pearson r             _______

5. Multiply the income of each male by $3,000. What is the new correlation coefficient?

                          Pearson r             _______

6. Does Pearson correlation coefficient change from question 1 to question 5? Explain.
7. Now suppose this income represents thousands of dollars lost in the stock market (instead of income earned). Multiply the income of each male by −1 (to change income to negative values). What is the new correlation coefficient?

                          Pearson r             _______

8. Now does Pearson correlation coefficient change (in question 7)? Explain.

Answer 1

Compute Pearson correlation coefficient for the data listed in the following table.

Add 3 inches to the height of each male. What is the new correlation coefficient?

Subtract $5,000 of income from each male. What is the new correlation coefficient?

Divide the height of each male in half. What is the new correlation coefficient?

Multiply the income of each male by $3,000. What is the new correlation coefficient?

Does Pearson correlation coefficient change from question 1 to question 5? Explain.

Correlation coefficient remains the same value 0.58 for all except subtraction of income with 5000.

Question 3 ( subtraction of 5000) only showing negative correlation -0.58

Now suppose this income represents thousands of dollars lost in the stock market (instead of income earned). Multiply the income of each male by −1 (to change income to negative values). What is the new correlation coefficient?

8. Now does Pearson correlation coefficient change (in question 7)? Explain.

Value does not change but it shows negative correlation -0.58