# Question

Regress Y against X with the following data from a random sample of 15 observations:

X Y

12 .............. 100

4 ............... 60

10 .............. 96

15 .............. 102

6 ............... 68

4 ............... 70

13 .............. 102

11 .............. 92

10 .............. 95

18 .............. 125

20 .............. 134

22 .............. 133

8 ............... 87

20 ................ 122

11 .............. 101

a. What is the regression equation?

b. What is the 90% confidence interval for the slope?

c. Test the null hypothesis “X does not affect Y” at an α of 1%.

d. Test the null hypothesis “the slope is zero” at an α of 1%.

e. Make a point prediction of Y when X = 10.

f. Assume that the value of X is controllable. What should be the value of X if the desired value for Y is 100?

g. Construct a residual plot. Are the residuals random?

h. Construct a normal probability plot. Are the residuals normally distributed?

X Y

12 .............. 100

4 ............... 60

10 .............. 96

15 .............. 102

6 ............... 68

4 ............... 70

13 .............. 102

11 .............. 92

10 .............. 95

18 .............. 125

20 .............. 134

22 .............. 133

8 ............... 87

20 ................ 122

11 .............. 101

a. What is the regression equation?

b. What is the 90% confidence interval for the slope?

c. Test the null hypothesis “X does not affect Y” at an α of 1%.

d. Test the null hypothesis “the slope is zero” at an α of 1%.

e. Make a point prediction of Y when X = 10.

f. Assume that the value of X is controllable. What should be the value of X if the desired value for Y is 100?

g. Construct a residual plot. Are the residuals random?

h. Construct a normal probability plot. Are the residuals normally distributed?

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