Consider the following data for a dependent variable y and two independent variables, x1 and x2.
x1 x2 y
30 12 94
47 10 108
25 17 112
51 16 178
40 5 94
51 19 175
74 7 170
36 12 117
59 13 142
76 16 211
The estimated regression equation for the data is ŷ = −18.4 + 2.01x1 + 4.74x2.
(a) Develop a 95% confidence interval for the mean value of y when x1 = 65 and x2 = 10. (Round your answers to three decimal places.) _______ to _______
(b) Develop a 95% prediction interval for y when x1 = 65 and x2 = 10. (Round your answers to three decimal places.) _______ to _______
Excel regression output is given below(Megastat)
Regression Analysis | |||||||
R² | 0.926 | ||||||
Adjusted R² | 0.904 | n | 10 | ||||
R | 0.962 | k | 2 | ||||
Std. Error | 12.710 | Dep. Var. | y | ||||
ANOVA table | |||||||
Source | SS | df | MS | F | p-value | ||
Regression | 14,052.1550 | 2 | 7,026.0775 | 43.50 | .0001 | ||
Residual | 1,130.7450 | 7 | 161.5350 | ||||
Total | 15,182.9000 | 9 | |||||
Regression output | confidence interval | ||||||
variables | coefficients | std. error | t (df=7) | p-value | 95% lower | 95% upper | |
Intercept | -18.3683 | ||||||
x1 | 2.0102 | 0.2471 | 8.134 | .0001 | 1.4258 | 2.5945 | |
x2 | 4.7378 | 0.9484 | 4.995 | .0016 | 2.4951 | 6.9805 | |
Predicted values for: y | |||||||
95% Confidence Interval | 95% Prediction Interval | ||||||
x1 | x2 | Predicted | lower | upper | lower | upper | Leverage |
65 | 10 | 159.672 | 145.203 | 174.141 | 126.317 | 193.027 | 0.232 |
from the output
a)
95% Confidence Interval | |
lower | upper |
145.203 | 174.141 |
b)
95% Prediction Interval | |
lower | upper |
126.317 | 193.027 |
Consider the following data for a dependent variable y and two independent variables, x1 and x2....
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