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?