Reading 11- LOS F (Part 2): Q17 class, 2008, following, equation, style

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17.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 percent confidence interval for the slope coefficient, b₁, is:

A)   {-0.766 < b₁ < 3.406}.

B)   {0.900 < b₁ < 1.740}.

C)   {0.444 < b₁ < 2.196}.

D)   {0.480 < b₁ < 2.160}.

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The correct answer was C)

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}.