Question

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.

(a) Compute R². (Round your answer to three decimal places.)

R² = ______

(b) Compute R_a². (Round your answer to three decimal places.)

R_a² = ______

Answer 1

(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.) ______

Answer

• 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.)______

Answer

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.

(a) Compute R². (Round your answer to three decimal places.)

R² = ______

Answer

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

(b) Compute R_a². (Round your answer to three decimal places.)

R_a² = ______ adjusted R square R_a²  

is 0.904

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.962042149
R Square	0.925525096
Adjusted R Square	0.904246551
Standard Error	12.70964216	0 0 Add a comment Know the answer? Your Answer: Post as a guest Your Name: What's your source? Earn Coins Coins can be redeemed for fabulous gifts. Log In Sign Up Post as anonymous Post Your Answer Not the answer you're looking for? Ask your own homework help question Similar Questions A statistical program is recommended. Consider the following data for a dependent variable y and two... A statistical program is recommended. 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... Consider the following data for a dependent variable y and two independent variables, x1 and x2... 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