In: Math
Consider the following data for a dependent variable y and two independent variables, x1 and x2.
x1 | x2 | y |
30 | 13 | 95 |
46 | 10 | 108 |
25 | 18 | 113 |
50 | 16 | 179 |
40 | 5 | 95 |
51 | 20 | 176 |
74 | 7 | 170 |
36 | 12 | 117 |
59 | 13 | 142 |
77 | 16 | 211 |
Round your all answers to two decimal places. Enter negative values as negative numbers, if necessary.
a. Develop an estimated regression equation relating y to x1.
ŷ =_________ +___________ x1
Predict y if x1 = 45.
ŷ = ____________
b. Develop an estimated regression equation relating y to x2.
ŷ =__________ +____________ x2
Predict y if x2 = 15.
ŷ = ___________
c. Develop an estimated regression equation relating y to x1 and x2.
ŷ =________ +___________ x1________ +____________ x2
Predict y if x1 = 45 and x2 = 15.
ŷ = __________
a)
Regression Statistics | ||||||
Multiple R | 0.8090 | |||||
R Square | 0.6545 | |||||
Adjusted R Square | 0.6113 | |||||
Standard Error | 25.5286 | |||||
Observations | 10 | |||||
ANOVA | ||||||
df | SS | MS | F | Significance F | ||
Regression | 1 | 9876.7 | 9876.7 | 15.16 | 0.0046 | |
Residual | 8 | 5213.7 | 651.7 | |||
Total | 9 | 15090.4 | ||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
Intercept | 47.4305 | 25.2577 | 1.8779 | 0.0972 | -10.8139 | 105.6748 |
X | 1.9092 | 0.4904 | 3.8930 | 0.0046 | 0.7783 | 3.0401 |
Ŷ = 47.43 +
1.91 *x
Predicted Y at X= 45 is
Ŷ = 47.4305 +
1.9092 * 45 =
133.35
b)
Regression Statistics | ||||||
Multiple R | 0.4273 | |||||
R Square | 0.1826 | |||||
Adjusted R Square | 0.0804 | |||||
Standard Error | 39.2673 | |||||
Observations | 10 | |||||
ANOVA | ||||||
df | SS | MS | F | Significance F | ||
Regression | 1 | 2755.0 | 2755.0 | 1.79 | 0.2181 | |
Residual | 8 | 12335.4 | 1541.9 | |||
Total | 9 | 15090.4 | ||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
Intercept | 92.5901 | 38.0028 | 2.4364 | 0.0408 | 4.9554 | 180.2248 |
X | 3.6931 | 2.7628 | 1.3367 | 0.2181 | -2.6780 | 10.0642 |
Ŷ = 92.59 +
3.69 *x
Predicted Y at X= 15 is
Ŷ = 92.5901 +
3.6931 * 15 =
147.99
c)
SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.957381 | |||||||
R Square | 0.916579 | |||||||
Adjusted R Square | 0.892744 | |||||||
Standard Error | 13.41035 | |||||||
Observations | 10 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 2 | 13831.54 | 6915.769 | 38.45567 | 0.000168 | |||
Residual | 7 | 1258.862 | 179.8374 | |||||
Total | 9 | 15090.4 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | -16.3966 | 19.00773 | -0.86263 | 0.416915 | -61.3427 | 28.54957 | -61.3427 | 28.54957 |
x1 | 2.03232 | 0.258959 | 7.848043 | 0.000103 | 1.419979 | 2.64466 | 1.419979 | 2.64466 |
x2 | 4.447643 | 0.948435 | 4.689455 | 0.002236 | 2.204951 | 6.690336 | 2.204951 | 6.690336 |
Y^ = -16.40+2.03*X1 + 4.45*X2
Y^ = -16.40+2.03*45 + 4.45*15 = 141.70