The following regression output was obtained from a study of architectural firms. The dependent variable is...

Question

Question

The following regression output was obtained from a study of architectural firms. The dependent variable is...

The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars.

Predictor	Coefficient		SE Coefficient		t		p-value
Constant		9.048		3.135		2.886		0.010
x₁		0.284		0.111		2.559		0.000
x₂	−	1.116		0.581	−	1.921		0.028
x₃	−	0.194		0.189	−	1.026		0.114
x₄		0.583		0.336		1.735		0.001
x₅	−	0.025		0.026	−	0.962		0.112

Analysis of Variance
Source	DF	SS	MS	F	p-value
Regression	5	1,895.93	379.2	6.46	0.000
Residual Error	44	2,581.75	58.68
Total	49	4,477.68

x₁ is the number of architects employed by the company.

x₂ is the number of engineers employed by the company.

x₃ is the number of years involved with health care projects.

x₄ is the number of states in which the firm operates.

x₅ is the percent of the firm’s work that is health care−related.

Write out the regression equation. (Negative answers should be indicated by a minus sign. Round your answers to 3 decimal places.)

How large is the sample? How many independent variables are there?

c-1. At the 0.05 significance level, state the decision rule to test: H₀: β₁ = β₂ = β₃ =β₄ = β₅ = 0; H₁: At least one β is 0. (Round your answer to 2 decimal places.)

c-2. Compute the value of the F statistic. (Round your answer to 2 decimal places.)

c-3. What is the decision regarding H₀: β₁ = β₂ = β₃ = β₄ = β₅ = 0?

d-1. State the decision rule for each independent variable. Use the 0.05 significance level. (Round your answers to 3 decimal places.)

For x₁	For x₂	For x₃	For x₄	For x₅
H₀: β₁ = 0	H₀: β₂ = 0	H₀: β₃ = 0	H₀: β₄ = 0	H₀: β₅ = 0
H₁: β₁ ≠ 0	H₁: β₂ ≠ 0	H₁: β₃ ≠ 0	H₁: β₄ ≠ 0	H₁: β₅ ≠ 0

d-2. Compute the value of the test statistic. (Negative answers should be indicated by a minus sign. Round your answers to 3 decimal places.)

d-3. For each variable, make a decision about the hypothesis that the coefficient is equal to zero.

math Statistics-And-Probability

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

regression equation
y^ = 9.048 + 0.284 *x1 - 1.116 x2 -0.194*x3 +0.583*x4 -0.025x5
How large is the sample? How many independent variables are there?
sample size = 50
independenet variable = 5
c1)

decison rule p-value < 0.05
c2)
F =6.46
c3)
p-value = 0.000 < 0.05
hence we reject the null

Add a comment

Answer 2

Similar Homework Help Questions

The following regression output was obtained from a study of architectural firms. The dependent variable is...

The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars. Predictor Coefficient SE Coefficient t p-value Constant 7.987 2.967 2.690 0.010 x1 0.122 0.031 3.920 0.000 x2 − 1.120 0.053 − 2.270 0.028 x3 − 0.063 0.039 − 1.610 0.114 x4 0.523 0.142 3.690 0.001 x5 − 0.065 0.040 − 1.620 0.112 Analysis of Variance Source DF SS MS F p-value Regression 5 371000 742...
PLEASE ROUND TO THE DECIMAL PLACES GIVEN. The following regression output was obtained from a study...

PLEASE ROUND TO THE DECIMAL PLACES GIVEN. The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars. Predictor Constant X2 Coefficient 9.387 0.232 -1.214 -0.273 0.642 -0.060 SE Coefficient 3.069 0.204 0.584 0.424 0.362 0.028 p-value 0.010 0.000 0.028 0.114 0.001 0.112 3.059 1. 137 -2.079 -0.644 1.773 -2.143 x3 X4 Analysis of Variance Source DF SS Regression 5 2,364.50 Residual Error 53 2,436.07 Total...
In a multiple regression analysis, k = 5 and n = 26, the MSE value is...

In a multiple regression analysis, k = 5 and n = 26, the MSE value is 9.99, and SS total is 402.22. At the 0.05 significance level, can we conclude that any of the regression coefficients are not equal to 0? (Round your answers to 2 decimal places.) H0: β1 = β2 = β3 = β4 = β5 = 0 H1: Not all β's equal zero. 1) DF1= 2) DF2= 3) Ho is rejected if F > = 4) Regression...

You may need to use the appropriate technology to answer this question. In a regression analysis ...

You may need to use the appropriate technology to answer this question. In a regression analysis involving 27 observations, the following estimated regression equation was developed. ŷ = 25.2 + 5.5x1 For this estimated regression equation SST = 1,550 and SSE = 550. (a) At α = 0.05, test whether x1 is significant. State the null and alternative hypotheses. H0: β1 = 0 Ha: β1 ≠ 0H0: β0 = 0 Ha: β0 ≠ 0 H0: β1 ≠ 0 Ha: β1...
Use the Excel output in the below table to do (1) through (6) for each ofβ0,...

Use the Excel output in the below table to do (1) through (6) for each ofβ0, β1, β2, and β3. y = β0 + β1x1 + β2x2 + β3x3 + ε df = n – (k + 1) = 16 – (3 + 1) = 12 Excel output for the hospital labor needs case (sample size: n = 16) Coefficients Standard Error t Stat p-value Lower 95% Upper 95% Intercept 1946.8020 504.1819 3.8613 0.0023 848.2840 3045.3201 XRay (x1) 0.0386...
Use the following linear regression equation to answer the questions. x1 = 1.5 + 3.4x2 – 8.3x3 + 2.3x4 (a) Which variable is the response variable? Which variables are the explanatory variables? (b...

Use the following linear regression equation to answer the questions. x1 = 1.5 + 3.4x2 – 8.3x3 + 2.3x4 (a) Which variable is the response variable? Which variables are the explanatory variables? (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant? x2 coefficient? x3 coefficient? x4 coefficient? (c) If x2 = 1, x3 = 8, and x4 = 6, what is the predicted value for x1? (Use 1 decimal place.) (d) Explain how...

Suppose a statistician built a multiple regression model for predicting the total number of runs scored...

Suppose a statistician built a multiple regression model for predicting the total number of runs scored by a baseball team during a season. Using data for n=200 samples, the results below were obtained. Complete parts a throughd. Ind. Var.Ind. Var. β estimate Standard Error Ind. Var. β estimate Standard Error InterceptIntercept 3.88 17.03 Doubles (x3) 0.74 0.04 Walks (x1) 0.37 0.05 Triples (x4) 1.17 0.23 Singles (x2) 0.51 0.05 Home Runs x5 1.44 0.04 a. Write the least squares prediction...
Suppose that we want to find a regression equation relating systolic blood pressure (y) to weight...

Suppose that we want to find a regression equation relating systolic blood pressure (y) to weight (x1), age (x2) and smoking status (0 = does not smoke, 1 = smokes less than one pack per day, 2 = smokes one or more packs per day). Use the Minitab outputs below to test whether or not the smoking status variable adds to the predictive value of a model which already contains weight and age, using α = .05. i.e., test the...
In a multiple regression analysis, two independent variables are considered, and the sample size is 26....

In a multiple regression analysis, two independent variables are considered, and the sample size is 26. The regression coefficients and the standard errors are as follows. b1 = 1.468 Sb1 = 0.89 b2 = −1.084 Sb2 = 0.88 Conduct a test of hypothesis to determine whether either independent variable has a coefficient equal to zero. Would you consider deleting either variable from the regression equation? Use the 0.05 significance level. (Negative amounts should be indicated by a minus sign. Round...

All Greens is a franchise store that sells house plants and lawn and garden supplies. Although Al...

All Greens is a franchise store that sells house plants and lawn and garden supplies. Although All Greens is a franchise, each store is owned and managed by private individuals. Some friends have asked you to go into business with them to open a new All Greens store in the suburbs of San Diego. The national franchise headquarters sent you the following information at your request. These data are about 27 All Greens stores in California. Each of the 27...

The following regression output was obtained from a study of architectural firms. The dependent variable is...

Homework Answers

Add Answer to:
The following regression output was obtained from a study of architectural firms. The dependent variable is...

Post as a guest

Earn Coins