Practice exam #1:

Here's the story: Your dog, Momo, barks way too much and you can't figure out why. One day, you forget to give Momo doggie biscuits and you notice that she does not bark that day. After thinking about this issue for a bit, you decide to run a study using 3 other dogs to determine whether # of doggie biscuits consumed is indeed related to the amount of barking. In this study you measure (X) the number of doggie biscuits each dog eats in a day and (Y) the number of times that dog barks, in order to see what the actual relationship is between these two variables.

X (# of doggie biscuits consumed) Y (# of barks in a day)

0 2

1 1

2 3

1. Create a frequency table for X.

2. Create a frequency histogram for X.

3. Compute the following:

Mean for X: Mean for Y:

Median for X: Median for Y:

Mode for X: Mode for Y:

SSx: SSy:

SDx²: SDy²:

SDx: SDy:

4. What is Zx when X = 0?

5. If Zy = 1.4, what would be the corresponding Y value?

6. What is the sum of the cross product of Z scores between X and Y?

7. What is the correlation (r) between X and Y?

8. Write the Z-score prediction model to predict Zy from Zx.

9. What is the predicted Zy if Zx = 0?

10. Write the raw-score prediction model to predict Y from X.

11. Draw scatterplot of raw data showing the correlation between X and Y.

12. The scatterplot shows that the relationship between X and Y is

A. very strong and positive.

B. very strong and negative.

C. moderate and positive.

D. moderate and negative.

13. Draw the regression line on the scatterplot up above.

14. Compute the proportionate reduction of error (NOT by just squaring "r").

15. Based on the proportionate reduction of error, what would you conclude about how well X predicts Y? EXPLAIN.

ANSWER KEY:

X - M (X-M) (X-M) ² Zx

0 - 1 -1 1 -1.22

1 - 1 0 0 0

2 - 1 1 1 1.22

___________________________________

Mx = 1 SSx = 2

SDx² = .67

SDx = .82

Y - M (Y-M) (Y-M) ² Zy

2 - 2 0 0 0

1 - 2 -1 1 -1.22

3 - 2 1 1 1.22

___________________________________

My = 2 SSy = 2

SDy² = .67

SDy = .82

ZxZy

-1.22*0 = 0

0*-1.22 = 0

1.22*1.22= 1.49

___________________

S(ZxZy) = 1.49

r = 1.45/3 = .50

Z score model ----> Zy(hat) = (.50)(Zx)

Raw score model ---->

b = .50(.82/.82) = .50

a = 2 - (1)(.50) = 1.50

----> Y` = 1.50 + .50(X)

Zy (predicted) if Zx = 0 ... Zy = 0

r² = (SSt - SSe)/SSt ...

Error Error²

Y Y` (Y- Y`) (Y- Y`)²

2 1.50 .50 .25

1 2 -1 1

3 2.50 .50 .25

____________________________________________

SSe = S(Y- Y`)² = 1.5

-- SSt = SSy = 2

r² = (SSt - SSe)/SSt = (2-1.5)/2 = .5/2 = 1/2*1/2 = .25

(r² = .50*.50 = .25)