lime remaining: 2:02:28 value: 10.00 points For a sample of 41 New England citie
ID: 3315037 • Letter: L
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lime remaining: 2:02:28 value: 10.00 points For a sample of 41 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1 ,000s). A portion of the regression results are shown in the following table ANOVA df MS Significance F 7.6E-06 Regression 2 3,557,706 1,778,853 16.33168 Residual 38 4,138,976 108,920.4 Total 40 7,696,682 a. Calculate the standard error of the estimate. (Round your answer to 2 decimal places.) b-1. What proportion of the sample variation in crime rate is explained by the variability in the explanatory variables? (Round your answer to 4 decimal places.) Explained proportion b-2. What proportion is unexplained? (Round your answer to 4 decimal places.) Unexplained proportion eBook & Resources eBo eBook: Calculate and interpret standard estimateExplanation / Answer
Here we have given ANOVA table for regression.
a) Here we have to find standard error of the estimate.
We know that the standard error formula is,
Standard error = sqrt(SSE/n-2)
where SSE is sum of squares due to error = 4138976
n we can find by using degrees of freedom for total.
We know that degrees of freedom for total = n-1
40 = n-1
n = 41
Standard error = sqrt(4166091/29-2) = sqrt(4138976/39) = 325.77
b) In the next part we have to find R2.
R2 = SSR / SST
where SSR is the sum of squares due to regression.
SST is the sum of squares due to total.
R2 = 3557706 / 7696682 = 0.4622 or 46.22%
The proportion of variability in crime rate is explained by the variability in the explanatory variables is 46.22%.
c) Unexplained variation = 1 - R2 = 1 - 0.4622 = 0.5378 = 53.78%
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