Let's assume that we want to look at the relationship between two variables, height (in inches) and self-esteem. Perhaps we have a hypothesis that how tall you are, affects your self-esteem. Let's also say we collected some information on 20 individuals (allmaleweknow that average height differs for males and females so, to keep this example simple we'll just use males).Self-esteem is measured based on the average of 10 1-to-5 rating items (where higher scores mean higher self-esteem).

Here's the data for the 20 cases:

Height Self Esteem

Person X Y

1 68 4.1

2 71 4.6

3 62 3.8

4 75 4.4

5 58 3.2

6 60 3.1

7 67 3.8

8 68 4.1

9 71 4.3

10 69 3.7

11 68 3.5

12 67 3.2

13 63 3.7

14 62 3.3

15 60 3.4

16 63 4.0

17 65 4.1

18 67 3.8

19 63 3.4

20 61 3.6

1. What is R-squared?Multiple R-squared?

2. Is the relationship significant?What is the value of the F-test, and the associated p-value?

3. What is the value of the intercept?Of height (X)?

4. How does self-esteem change with height?How much per inch of height?

5. If a male whose height is 66 inches, what would his estimated self-esteem be, according to the regression equation?