Question

# 8. Consider the following data for a dependent variable y and two independent variables, x1 and...

8. 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

(a) Develop an estimated regression equation relating y to x1. (Round your numerical values to one decimal place.)

ŷ = ______

Predict y if x1 = 51. (Round your answer to one decimal place.)

______

(b) Develop an estimated regression equation relating y to x2. (Round your numerical values to one decimal place.)

ŷ = ______

Predict y if x2 = 16. (Round your answer to one decimal place.)

______

(c) Develop an estimated regression equation relating y to x1 and x2. (Round your numerical values to one decimal place.)ŷ =

Predict y if x1 = 51 and x2 = 16. (Round your answer to one decimal place.)

______

9. Ten observations were provided for a dependent variable y and two independent variables x1 and x2; for these data,

SST = 15,188.8 and SSR = 14,056.7.

R2 = ______

Ra2 = ______

(a) Develop an estimated regression equation relating y to x1. (Round your numerical values to one decimal place.)

ŷ = ______

Predict y if x1 = 51. (Round your answer to one decimal place.) ______

• Assume y = ax1 + b where b is the intercept and a is the intercept.
• Just put the sample set on excel , click data tab , data analysis and select regression.
• Apply y vs x1 data and below are the results.
 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
 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 = ax1 + 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 x2. (Round your numerical values to one decimal place.)

ŷ = ______

Predict y if x2 = 16. (Round your answer to one decimal place.)______

Same approach as in part a)

y = ax2 + 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 = ax2 + b

y = 85.21 + 4.32x2

at x2 = 16 , y = 85.21 + 4.32*16 = 154.33

(c) Develop an estimated regression equation relating y to x1 and x2. (Round your numerical values to one decimal place.)ŷ =

Predict y if x1 = 51 and x2 = 16. (Round your answer to one decimal place.)

• Let the final equation is y = ax1 + bx2 + c
• Now as per regression run on excel a= 2.01 , b = 4.73 and c = -18.36
• Hence , final equation is y = 2.01x1 + 4.73x2 -18.36
• Predict y if x1 = 51 and x2 = 16.
• y = 2.01*51 + 4.73*16 -18.36 =159.83

9. Ten observations were provided for a dependent variable y and two independent variables x1 and x2; for these data,

SST = 15,188.8 and SSR = 14,056.7.

R2 = ______

R2 = SSR/SST = 14,056.7/ 15,188.8 = 0.925

Ra2 = ______ adjusted R square Ra2

is 0.904

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.962042149
R Square 0.925525096
Standard Error 12.70964216

#### Earn Coins

Coins can be redeemed for fabulous gifts.