Question

Use the following information for Problems 31-33. (You could verify your answers in SPSS, but I would like to see your hand calculations)

Subject           Test X   Test Y

   1                      10          10

   2                      6             8

   3                      6             9

   4                      5             4

   5                      6             10

6                      7 11

7                      9 10

8                      7 9

31. Compute the following values.

   

(a) r (X,Y) = _________

(b) Using the result from (a) compute S_Y.X = ___________________

(c) Interpret your result to part (b)

32. (a) Using the data above, determine the regression equation to predict Test Y performance

        from the Test X performance.

Regression equation: __________________________

(b) Carefully construct a scatter plot using grid paper and label the regression line. Make sure to LABEL your axes. Insert a copy of your plot in the space provided below. (2 points)

(c) Interpret the slope of the regression line. (1 point)

           

33. Using the regression equation from the previous problem,

a) What score on Test Y would you predict for someone who scored 5 on Test X?

_________________

            b) How much predictive error is there for the Subject who scored 5 on Test X?

            ________________

Answer 1

Question 31 :

Consider X : Score of Test X.

Y : Score of Test Y.

a) Correlation coefficient between X and Y is

Where

X	Y	X2	Y2	XY
10	10	100	100	100
6	8	36	64	48
6	9	36	81	54
5	4	25	16	20
6	10	36	100	60
7	11	49	121	77
9	10	81	100	90
7	9	49	81	63
56	71	412	663	512

Hence correlation coefficient between X and Y is

b) From part (a)

c) Since value of S_xy > 0 . There is positive correlation between X and Y.

Question 32.

The regression equation Y on X is

Y = a + b X

Where a is Y-intercept and b is slope of the line.

The values of a and b are

a = 3.625

The regression equation is

Y = 3.625+ 0.75 *X

b) Scatter Plot.

c) The slope of the regression line b = 0.75

If the score of Test X increased by 1 unit, then we predict the score of test Y will be increased by 0.75 unit.

Question 33 :

a) We have to find value of Y when X = 5.

By using regression equation

Yhat = a + b * 5 = 3.625 + 0.75 * 5 = 7.375

Yhat = 7.375

b) Observed value of Y when X =5 is Yobs = 4

and predicted value of Y when X = 5 is Yhat = 7.375

Predicted error is

e = Yobs - Yhat = 4-7.375 = -3.375