7. Given the following estimated regression line Y = 10.0 + 6.0 x X. R2 0.40, SER = 2.0, n = 500 (8.0) (4.0) %3D The standard errors are in the parentheses (1) Construct a 99% two-sided confidence interval for the slope coefficient (B,) Alpha=1-(99/100) =0.01 Critical probability 1-(alpha/2) =1-0.005%-D0.995 df = n-2 = 500 - 2=498 %3D (2) Construct a 95% two-sided confidence interval for the intercept coefficient (Bo).
7. Given the following estimated regression line Y = 10.0 + 6.0 x X. R2 0.40, SER = 2.0, n = 500 (8.0) (4.0) %3D The standard errors are in the parentheses (1) Construct a 99% two-sided confidence interval for the slope coefficient (B,) Alpha=1-(99/100) =0.01 Critical probability 1-(alpha/2) =1-0.005%-D0.995 df = n-2 = 500 - 2=498 %3D (2) Construct a 95% two-sided confidence interval for the intercept coefficient (Bo).
Chapter1: Making Economics Decisions
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7. Given the following estimated regression line
Y = 10.0 + 6.0 x X. R2 = 0.40, SER = 2.0, n = 500
(8.0) (4.0)
The standard errors are in the parentheses
(1) Construct a 99% two-sided confidence interval for the slope coefficient (B,)
Alpha=1-(99/100) =0.01
Critical probability = 1-(alpha/2) =1-0.005-0.995
df = n-2 = 500 – 2 =498
(2) Construct a 95% two-sided confidence interval for the intercept coefficient (Bo).
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Step 1
Answer: (1)
α = 1 - (confidence level / 100) = 1 - (99/100) = 0.01
The critical probability = p* = 1 - α/2 = 1 - (0.01/2) = 0.995
The degrees of freedom (df):
df = n - 2 = 500 - 2 = 498
The critical value is the t statistic having 498 degrees of freedom and a cumulative probability equal to 0.995.
From the t- value calculator, the critical value is 0.0062698
Computing the margin of error (ME):
ME = critical value * standard error
ME = 0.0062698 * 4.0 = 0.0250792
The range of the confidence interval is equal to the sample statistic plus and minus margin of error.
Therefore, the 99% confidence interval for this sample is 6.0 0.0250792, which is 5.975 to 6.025
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