A researcher is analyzing whether the rate of unlawful breaking and entering of vehicles is affected by the percentage of poverty, percentage male, percentage non-White, and the percentage of individuals between the ages of 15 and 24 residing in the census block. Given the following SPSS output, what would the researcher conclude? State the null and alternative hypotheses, discuss the F statistic, the R2, R2 change, the beta coefficients, and which variable significantly affect the dependent variable.

Question

What will be an ideal response?

Answer 1

H0 : ?1, ?2, ?3, ?4 = 0 or R2 = 0
H1 : ?1, ?2, ?3, ?4 ? 0 or R2 ? 0

The calculated F statistics is larger than the critical F statistic indicating that the model is significant and the slope coefficients when used together predict the dependent variable are not equal to zero. The R2 in Model 1 explains 3.8% of the variation in the dependent variable while the two variables entered into Model 2 explains 12.8% of the variation in the dependent variable. When all variables are included in the model, 16.6% of the variation in the dependent variable is explained. Of the four variables in the regression equation, percentage male has the largest impact on the dependent variable, followed by percentage in poverty, percentage between the ages of 15 and 24, and finally percentage non-White. Three of the four measures are significant at the .05 alpha level. Percentage in poverty, percentage male, and the percentage between the ages of 15 and 24 are significant predictors of unlawful breaking and entering of vehicles. The null hypothesis would be rejected for those three variables and accepted for percentage non-White.