To see if attractiveness is related to how often (that is, how many people help) women receive help from strangers, five women of varying levels attractiveness took turns standing next to a stalled car for one hour.Researchers then rated the attractiveness (using an interval scale which ranged from 1=extremely unattractive to 10=extremely attractive) of the women and noted how often strangers offered help to each women.Their data are below:

Attractiveness (X)

Z score for attractiveness

Offers of help (Y)

Z score for offers of help

Person A

9

+1.49

6

+1.07

Person B

7

+0.66

4

-0.27

Person C

5

-0.17

6

+1.07

PersonD

4

-0.58

2

-1.6

PersonE

2

-1.40

4

-0.27

Mean

5.40

4.4

Standard Deviation

2.42

1.50

1 (3pts)Construct a scatterplot for these data

2(4pts)Compute the Pearson correlation coefficient between attractiveness and number of strangers offering help.(Note: For full points, at the end of this problem you should have computed a value, not just given anequation.).

3(4pts)According to your calculations, what proportion of variability in Y (offers of help) can be explained by variability in X (attractiveness)?(Note: For full points, at the end of this problem you should have computed a value, not just given an equation.)

4(5pts)Compute the linear equation (a regression equation) that best predicts the help (Y) based on attractiveness (X).(Note: at the end of this problem you should have an equation where two values - the constants -- in the equation are computed.)

5 (2pts)Plot your line (from the Problem 1.4) onto the scatterplot (from Problem 1.1).(Some free advice: You will be able to tell if the equation you got in Problem 1.4 is correct by seeing if your line reasonably fits the scatterplot such that the points above the line are about as far from the line as the points below the line.If it doesn't fit, you might have made a mistake with working on Problem 1.2 or 1.4.)

6(2pts)Based on the equation you found in 1.4, how many people would you predict would help (Y') Jessica Alba whose attractiveness score (X) is 10?

7 (3pts)Compute the standard error of prediction for help(Y) based on attractiveness (X).

8 (2pts)Interpret Problem 1.7 above.What does the value you computed tell you about your predictions for the number of people who would offer help?

9(5pts)Now compute a linear regression equation that predicts attractiveness (X)

based on help (Y). Note that this equation should be similar in shape with your

answer for 1.4 but should have different values asconstants.

(Bonus question)

10(3pts)1) Compute the standard error of prediction for attractiveness (X) based on help

(Y), and 2) compare the value (the results of your computation) with the

standard error of prediction for help (Y) based on attractiveness (X), and explain

why they are different when they are both computed based on the same

correlation between attractiveness and help