Question

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		7.617			2.998			2.541			0.010
x1		0.224			0.069			3.246			0.000
x2	?	1.144			0.559		?	2.047			0.028
x3	?	0.071			0.120		?	0.592			0.114
x4		0.675			0.354			1.907			0.001
x5	?	0.057			0.025		?	2.280			0.112

Analysis of Variance
Source	DF		SS		MS		F		p-value
Regression	5		2,113.40		422.7		7.37		0.000
Residual Error	48		2,751.10		57.31
Total	53		4,864.50

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: ?₁ = ?₂ = ?₃ =?₄ = ?₅ = 0; H₁: At least one ? 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: ?₁ = ?₂ = ?₃ = ?₄ = ?₅ = 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: ?1 = 0		H0: ?2 = 0		H0: ?3 = 0		H0: ?4 = 0		H0: ?5 = 0
H1: ?1 ? 0		H1: ?2 ? 0		H1: ?3 ? 0		H1: ?4 ? 0		H1: ?5 ? 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.

Answer 1

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

y=7.617+0.224x1-1.144x2-0.071x3+0.675x4-0.057x5

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

n=53+1=54

n=54

5 independent variables x1x2,x3,x4,x5

k=5(independent

c-1. At the 0.05 significance level, state the decision rule to test: H0: ?1 = ?2 = ?3 =?4 = ?5 = 0; H1: At least one ? is 0. (Round your answer to 2 decimal places.)

F=7.37

p=0.000

p<0.05

Reject null hypothesis.

Accept alternative Hypothesis.

At least one ? is 0

c-2. Compute the value of the F statistic

F=7.37

c-3. What is the decision regarding H0: ?1 = ?2 = ?3 = ?4 = ?5 = 0

Atleast one ? is 0

d-1. State the decision rule for each independent variable.

For x1 p=0.000,p<0.05

H1: ?1 ? 0

For x2 p=0.028,p<0.05 Reject Ho Accept H1

H1: ?2 ? 0

For x3,p=0.114,p>0.05 Accpet H0.

H0: ?3 = 0

For x4 ,p=0.001,p<0.05 Reject Ho

H1: ?4 ? 0

For x5 ,p=0.112,p>0.05Accept Ho

H0: ?5 = 0

d-2. Compute the value of the test statistic.

for x1 ,t=3.235

for x2 t=-2.047

for x3 t=-0.592

for x4 ,t=1.907

for x5,t=-2.280

Solutiond3:

x1,x2,x4 are significant variables as p<0.05

x3,x5 are non significant variables as p>0.05