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.

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.

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.)

	? = + x1 + x2 + x3 + x4 + x5

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

	Sample n Independent variables k

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

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
Reject H0 if t < not attempted or t > not attempted .

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.)

x1not attempted

x2not attempted

x3not attempted

x4not attempted

x5not attempted

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

x1not attempted

x2not attempted

x3not attempted

x4not attempted

x5not attempted

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+0.224*x1+1.144x2+0.071*x3+0.675*x4+0.057*x5

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

n=df+1=53+1=54,

5 independent variables are there .They are x1,x2,x3,x4,x5

n=54

k=5

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=0.00

Reject Ho as p<0.05

Accept H1.

c-2. Compute the value of the F statistic

F=7.37

d-1. State the decision rule for each independent variable. Use the 0.05 significance level. (Round

Reject Ho if t statistic<Tcritical or tstatistic greater than T crit.

value of the test statistic.

solutiond-2.

For x1 t=3.246

for x2 t=2.047

for x3 t=0.592

for x4 t=1.907

for x5 t=2.280

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

For x1 p=0.000,p<0.05 Reject Ho

for x2,p=0.028,p<0.05 Reject Ho

for x3,p=0.114,p>0.05 Fail to reject H0

for x4,p=0.001,p<0.05 Reject H0

for x5,0.112,p>0.05 Fail to Reject Ho