Use the chi-square test to determine whether there is any interaction between location and the tendency of residuals to be positive or negative. If you reject the null hypothesis of no pattern, describe how a researcher might continue the regression analysis.
The following table represents the number of residuals observed in a regression of voter
registration rates on income and age over eight districts:
First, we calculate the expected frequencies of the residuals, given the totals
We use these expected values to calculate the chi-square statistic. For each cell, we divide the
squared difference between the observed and expected values by the expected value: e.g. (20 -
17.7)2
/ 17.7. These values are summed, and their sum comes to 2.885.
We compare this value to the chi-square distribution, for which the critical value is associated with
the chosen alpha (0.05) and the degrees of freedom (the number of rows minus one times the
number of columns minus one, or 1 * 7 in this case for d.f. 7). 14.067 is larger than our chi-square
value of 2.885, so that we fail to reject the null hypothesis of no spatial pattern.
Given the lack of relationship between location and residuals, we need not take any further steps.
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The general form of a confidence interval is
a. Standard error ± critical value × estimated parameter value b. Critical value ± estimated parameter value × standard error c. Estimated parameter value ± standard error × critical value
The nineteenth-century civil rights acts were important because they __________.
A. established that Congress could not legislate directly against individuals in violation of others' constitutional rights B. affirmed the belief that congressional power applied to official or government action or to private action C. were not significant to the civil rights struggles of the 1960s D. introduced the legal consequence that if the federal government did not secure rights, the state governments could E. became effective immediately despite customary delays in implementation