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... Consider the following data for a dependent variable y and two independent variables, x1 and x2 . x 1 x 2 y 29 13 94 46 11 109 25 17 112 50 16 178 40 6 95 51 19 175 74 7 170 36 13 117 59 13 143 76 17 212 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... Consider the following data for a dependent variable y and two independent variables, x1 and x2.... Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 29 12 95 46 10 109 24 17 113 50 17 178 40 5 94 52 19 176 74 7 170 36 13 118 59 13 143 76 16 212 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. y^=_____ + _____x1 (fill in... Consider the following data for a dependent variable y and two independent variables,  x1 and x2. x1... 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 these data isŷ = −18.37 + 2.01x1 + 4.74x2. Here, SST = 15,182.9, SSR = 14,052.2, sb1 = 0.2471,  and  sb2 = 0.9484. (A) Test for a significant relationship... 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 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... Consider the following data for a dependent variable y and two independent variables, x1and x2; for... Consider the following data for a dependent variable y and two independent variables, x1and x2; for these data SST = 15,309.6, and SSR = 14,429.8. x 1 x 2 y 30 12   94 47 10 109 25 17 113 51 17 179 41   5   94 51 19 176 74   7 170 36 13 118 59 13 143 76 17 212 Round your answers to three decimal places. a. Compute R2. b. Compute Ra2. Consider the following data for a dependent variable y and two independent variables, x1and x2. x1... Consider the following data for a dependent variable y and two independent variables, x1and x2. x1 x2 y 30 12 96 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 these data is ŷ = −17.33 + 2.00x1 + 4.73x2. Here, SST = 15,002.1, SSR = 13,887.5, sb1 = 0.2454,and sb2 = 0.9417. (a)Test for a significant... The owner of a movie theater company used multiple regression analysis to predict gross revenue (y)... The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x1) and newspaper advertising (x2).The estimated regression equation was ŷ = 83.1 + 2.23x1 + 1.30x2. The computer solution, based on a sample of eight weeks, provided SST = 25.4 and SSR = 23.395. (a) Compute and interpret R2 and Ra2. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that... The owner of a movie theater company used multiple regression analysis to predict gross revenue (y)... The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x1) and newspaper advertising (x2). The estimated regression equation was ŷ = 82.5 + 2.26x1 + 1.30x2. The computer solution, based on a sample of eight weeks, provided SST = 25.3 and SSR = 23.415. (a)Compute and interpret R2 and Ra2. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that... The owner of a movie theater company used multiple regression analysis to predict gross revenue (y)... The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x1)  and newspaper advertising (x2).  The estimated regression equation was ŷ = 83.8 + 2.26x1 + 1.50x2. The computer solution, based on a sample of eight weeks, provided SST = 25.8 and SSR = 23.385. (a) Compute and interpret  R2 and Ra2. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that can be... ADVERTISEMENT Need Online Homework Help? Get Answers For Free Most questions answered within 1 hours. Ask a Question ADVERTISEMENT Active Questions Write the code in C# List the evens or the odds. You are given a lower... asked 5 minutes ago Draw a binary search tree with the following words (inserted in the provided order): Kenya, Austria,... asked 33 minutes ago There are the set of FD for a Relation R(A, B,C,D,E,F,G) F= (A->B, BC->DE, AEF->G, AC->DE)... asked 39 minutes ago Is a policy that would run deficits (surpluses) be best for today’s economy? Explain your answer. asked 44 minutes ago CSE 231                                         &n asked 51 minutes ago What are the benefits of using play as a therapy modality ? asked 52 minutes ago 1) Assume you have one end of an Ethernet cable in your hands and that connector... asked 52 minutes ago 1.A string with linear density 2.0 g/m is under 500 N of tension. What is the... asked 1 hour ago Give an pushdown automaton (PDA) that will accept the following language: {w ∈ {a, b}∗ |... asked 1 hour ago Use the Hazen-Williams equation and the Manning equation to calculate the flow rate for problem 3.5.7on... asked 1 hour ago Using JES/Jython Function Name: approachAllAngles() Parameters: Sides- integer of how many sides the shape has Using... asked 1 hour ago Why are data manipulation, efficiency, and memory useful in programming? Provide specific examples of data manipulation... asked 1 hour ago About Contact Terms of Use Privacy Policy Academic Honesty Policy Homework Answer Scanner App Report DMCA © 2022 JustAAA   user contributions licensed under cc by-sa 4.0