8. Consider the following data for a dependent variable y and two independent variables, x_{1} and x_{2}.
x_{1} |
x_{2} |
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 |
(a) Develop an estimated regression equation relating y to x_{1}. (Round your numerical values to one decimal place.)
ŷ = ______
Predict y if x_{1} = 51. (Round your answer to one decimal place.)
______
(b) Develop an estimated regression equation relating y to x_{2}. (Round your numerical values to one decimal place.)
ŷ = ______
Predict y if x_{2} = 16. (Round your answer to one decimal place.)
______
(c) Develop an estimated regression equation relating y to x_{1} and x_{2}. (Round your numerical values to one decimal place.)ŷ =
Predict y if x_{1} = 51 and x_{2} = 16. (Round your answer to one decimal place.)
______
9. Ten observations were provided for a dependent variable y and two independent variables x_{1} and x_{2}; for these data,
SST = 15,188.8 and SSR = 14,056.7.
(a) Compute R^{2}. (Round your answer to three decimal places.)
R^{2} = ______
(b) Compute R_{a}^{2}. (Round your answer to three decimal places.)
R_{a}^{2} = ______
(a) Develop an estimated regression equation relating y to x_{1}. (Round your numerical values to one decimal place.)
ŷ = ______
Predict y if x_{1} = 51. (Round your answer to one decimal place.) ______
Answer
x_{1} | x_{2} | 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 |
SUMMARY OUTPUT | |||||
Regression Statistics | |||||
Multiple R | 0.812425462 | ||||
R Square | 0.660035131 | ||||
Adjusted R Square | 0.617539523 | ||||
Standard Error | 25.40091683 | ||||
Observations | 10 | ||||
ANOVA | |||||
df | SS | MS | F | Significance F | |
Regression | 1 | 10021.24739 | 10021.24739 | 15.53184324 | 0.004289591 |
Residual | 8 | 5161.652607 | 645.2065758 | ||
Total | 9 | 15182.9 | |||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | |
Intercept | 45.05936899 | 25.41814558 | 1.772724483 | 0.114210782 | -13.55497982 |
x1 | 1.943571186 | 0.493161259 | 3.941045958 | 0.004289591 | 0.806339284 |
The final equation is y = ax_{1} + b
y = 45.05 + 1.94x1
at x1 = 51 , y = 45.05 + 1.94*51 = 143.99
(b) Develop an estimated regression equation relating y to x_{2}. (Round your numerical values to one decimal place.)
ŷ = ______
Predict y if x_{2} = 16. (Round your answer to one decimal place.)______
Answer
Same approach as in part a)
y = ax_{2} + b
SUMMARY OUTPUT | ||||
Regression Statistics | ||||
Multiple R | 0.47066598 | |||
R Square | 0.221526465 | |||
Adjusted R Square | 0.124217273 | |||
Standard Error | 38.43742616 | |||
Observations | 10 | |||
ANOVA | ||||
df | SS | MS | F | |
Regression | 1 | 3363.414159 | 3363.414159 | 2.276521469 |
Residual | 8 | 11819.48584 | 1477.43573 | |
Total | 9 | 15182.9 | ||
Coefficients | Standard Error | t Stat | P-value | |
Intercept | 85.21710161 | 38.35196208 | 2.221975018 | 0.057006207 |
x2 | 4.321488062 | 2.864161103 | 1.508814591 | 0.169781356 |
The final equation is y = ax_{2} + b
y = 85.21 + 4.32x_{2}
at x_{2} = 16 , y = 85.21 + 4.32*16 = 154.33
(c) Develop an estimated regression equation relating y to x_{1} and x_{2}. (Round your numerical values to one decimal place.)ŷ =
Predict y if x_{1} = 51 and x_{2} = 16. (Round your answer to one decimal place.)
9. Ten observations were provided for a dependent variable y and two independent variables x_{1} and x_{2}; for these data,
SST = 15,188.8 and SSR = 14,056.7.
(a) Compute R^{2}. (Round your answer to three decimal places.)
R^{2} = ______
Answer
R^{2} = SSR/SST = 14,056.7/ 15,188.8 = 0.925
(b) Compute R_{a}^{2}. (Round your answer to three decimal places.)
R_{a}^{2} = ______ adjusted R square R_{a}^{2 }
is 0.904