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2、In a regression analysis, the Central Limit Theorem (CLT)

A) is useful because it implies that the independent variables are normally distributed.

B) is useful because it implies that the estimators are BLUE (best linear unbiased estimators).

C) is not useful.

D) is useful because it implies that the residuals are normally distributed, which implies the coefficient estimates are normally distributed.

aianjie

 

The correct answer is D

The theory is that the residuals represent a large number of effects not captured by the included independent variables. Therefore, by the CLT, the residuals can be assumed normally distributed. Since the estimators are linear functions of the residuals, the estimates can be assumed normally distributed.

 

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AIM 6: Define, calculate and interpret hypothesis testing in an OLS regression model

1、Assume you ran a multiple regression to gain a better understanding of the relationship between lumber sales, housing starts, and commercial construction. The regression uses lumber sales as the dependent variable with housing starts and commercial construction as the independent variables. The results of the regression are:

	Coefficient	Standard Error	t-statistics
Intercept	5.37	1.71	3.14
Housing starts	0.76	0.09	8.44
Commercial construction	1.25	0.33	3.78
The level of significance for a 95% confidence level is 1.96

Construct a 95% confidence interval for the slope coefficient for Housing Starts.

A)    0.76 ± 1.96(0.09).

B)    0.76 ± 1.96(8.44).

C)   1.25 ± 1.96(0.33).

D)   1.25 ± 1.96(3.78).

aianjie

 

The correct answer is A

The confidence interval for the slope coefficient is b1 ± (tc × sb1).

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Construct a 95% confidence interval for the slope coefficient for Commercial Construction.

A) 1.25 ± 1.96(3.78).

B) 1.25 ± 1.96(0.33).

C) 0.76 ± 1.96(0.09).

D) 0.76 ± 1.96(8.44).

aianjie

 

The correct answer is B

The confidence interval for the slope coefficient is b1 ± (tc × sb1).

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2、Consider the following estimated regression equation:

AUTOt = 0.89 + 1.32 PIt

The standard error of the coefficient is 0.42 and the number of observations is 22. The 95 percent confidence interval for the slope coefficient, b1, is:

A) {-0.766 < b1 < 3.406}.

B) {0.900 < b1 < 1.740}.

C) {0.480 < b1 < 2.160}.

D) {0.444 < b1 < 2.196}.

aianjie

 

The correct answer is D

The degrees of freedom are found by n-k-1 with k being the number of independent variables or 1 in this case.  DF =  22-1-1 = 20.  Looking up 20 degrees of freedom on the student's t distribution for a 95% confidence level and a 2 tailed test gives us a critical value of 2.086.  The confidence interval is 1.32 ± 2.086 (0.42), or {0.444 < b1 < 2.196}.

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3、Consider the following estimated regression equation:

ROEt = 0.23 - 1.50 CEt

The standard error of the coefficient is 0.40 and the number of observations is 32. The 95 percent confidence interval for the slope coefficient, b1, is:

A) {0.683 < b1 < 2.317}.

B) {-2.300 < b1 < -0.700}.

C) {-2.317 < b1 < -0.683}.

D) {-3.542 < b1 < 0.542}.

aianjie

 

The correct answer is C

The confidence interval is -1.50 ± 2.042 (0.40), or {-2.317 < b1 < -0.683}.