Homework SourseExercise 1528 Use computer software packages such as Minitab
{Exercise 15.28}
Use computer software packages, such as Minitab or Excel, to solve this problem.
Consider the following data for a dependent variable y and two independent variables, x1 and x2.
The estimated regression equation for this data is
= -22.4+ 1.99x1 + 4.92x2
Round your answers to two decimal places.
a. Develop a 95% confidence interval for the mean value of y when x1 = 45 and x2 = 15.
95% confidence interval is _________________ to _________________ .
b. Develop a 95% prediction interval for y when x1 = 45 and x2 = 15.
95% prediction interval is _________________ to _________________ .
| x1 | x2 | y |
| 30 | 12 | 95 |
| 47 | 11 | 109 |
| 24 | 17 | 113 |
| 51 | 17 | 178 |
| 41 | 6 | 94 |
| 52 | 20 | 175 |
| 75 | 7 | 170 |
| 36 | 13 | 117 |
| 60 | 13 | 142 |
| 76 | 16 | 211 |
Solution
From excel, we get the following output -
| SUMMARY OUTPUT | ||||||||
| Regression Statistics | ||||||||
| Multiple R | 0.96517519 | |||||||
| R Square | 0.93156315 | |||||||
| Adjusted R Square | 0.91200976 | |||||||
| Standard Error | 12.0987836 | |||||||
| Observations | 10 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 2 | 13947.73604 | 6973.868 | 47.64203 | 8.38523E-05 | |||
| Residual | 7 | 1024.663961 | 146.3806 | |||||
| Total | 9 | 14972.4 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | -22.393849 | 17.70685058 | -1.2647 | 0.246455 | -64.26389772 | 19.4762 | -64.2639 | 19.4762 |
| x1 | 1.98798431 | 0.231291334 | 8.595153 | 5.75E-05 | 1.441067209 | 2.534901 | 1.441067 | 2.534901 |
| x2 | 4.9231077 | 0.906956759 | 5.428161 | 0.000979 | 2.778495749 | 7.06772 | 2.778496 | 7.06772 |
