Q5. Consider the following estimated regression equation:

ROE_t = 0.23 - 1.50 CE_t

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

A)      {-2.317 < b₁ < -0.683}.

B)     {0.683 < b₁ < 2.317}.

C)     {-2.300 < b₁ < -0.700}.

Q6. Consider the following estimated regression equation:

AUTO_t = 0.89 + 1.32 PI_t

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

A)     {-0.766 < b₁ < 3.406}.

B)     {0.444 < b₁ < 2.196}.

C)     {0.480 < b₁ < 2.160}.

Q7. 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:

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).

Q8. Construct a 95% confidence interval for the slope coefficient for Commercial Construction.

A)   1.25 ± 1.96(0.33).

B)   0.76 ± 1.96(0.09).

C)   1.25 ± 1.96(3.78).

答案和详解如下：

Q5. Consider the following estimated regression equation:

ROE_t = 0.23 - 1.50 CE_t

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

A)      {-2.317 < b₁ < -0.683}.

B)     {0.683 < b₁ < 2.317}.

C)     {-2.300 < b₁ < -0.700}.

Correct answer is A)

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

Q6. Consider the following estimated regression equation:

AUTO_t = 0.89 + 1.32 PI_t

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

A)     {-0.766 < b₁ < 3.406}.

B)     {0.444 < b₁ < 2.196}.

C)     {0.480 < b₁ < 2.160}.

Correct answer is B)

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}.

Q7. 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:

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).

Correct answer is A)

The confidence interval for the slope coefficient is b₁ ± (t_c × s_b1).

Q8. Construct a 95% confidence interval for the slope coefficient for Commercial Construction.

A)   1.25 ± 1.96(0.33).

B)   0.76 ± 1.96(0.09).

C)   1.25 ± 1.96(3.78).

Correct answer is A)

The confidence interval for the slope coefficient is b₁ ± (t_c × s_b1).

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