The following is the regression output for a study on seriouscrime rates in cities in the United States. The data was collectedin the 1970s. AREA is the size of the city, DOCS is the number ofDoctors, % > 65 is the proportion of residents greater than 65years of age and HOSPITAL BEDS is the number of hospital beds perpopulation. Answer the following questions given the suppliedregression output. These variables are regressed on the seriouscrime rates in an attempt to explain variance in crime rates indifferent cities. (3 points per question)
SUMMARY OUTPUT | | | | | | |
| | | | | | |
Regression Statistics | | | | | |
Multiple R | 0.673273 | | | | | |
R Square | 0.4532966 | | | | | |
Adjusted R Square | 0.4047007 | | | | | |
Standard Error | 12.033733 | | | | | |
Observations | 50 | | | | | |
| | | | | | |
ANOVA | | | | | | |
| df | SS | MS | F | Significance F | |
Regression | 4 | 5403.1119 | 1350.778 | 9.3278852 | 1.40799E-05 | |
Residual | 45 | 6516.4834 | 144.81074 | | | |
Total | 49 | 11919.595 | | | | |
| | | | | | |
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% |
Intercept | 66.550797 | 9.4140949 | 7.069272 | 8.044E-09 | 47.58983709 | 85.511758 |
AREA | 1.9887428 | 0.8666883 | 2.2946459 | 0.0264716 | 0.24314292 | 3.7343427 |
% > 65 | -1.368696 | 0.6703271 | -2.041833 | 0.0470559 | -2.718804364 | -0.018588 |
DOCS | 8.6790607 | 3.3369629 | 2.6008862 | 0.1125379 | 1.958072413 | 15.400049 |
HOSP BEDS | -2.407649 | 0.7129517 | -3.377016 | 0.0015198 | -3.843607893 | -0.971691 |
- How accurate is regression model? What amount of the variancein Serious Crimes is explained
- How strong is the linear relationship between the predictorsand Serious Crimes?
- How close to the regression line is the majority ofobservations?
- Does the model fit the data better than not using thesepredictor variables? Is the F-test significant? What hypothesis canwe draw from it?
- Use the output to form the regression equation.
- Are all the predictors significant? Is zero contained in theconfidence intervals? Why is that interesting?
- Of the significant variables, does the corresponding slopesmake intuitive sense? Are the effects of the predictorsreasonable?
- How much variance in serious crime is unaccounted for? Whatadditional data might explain some of this remaining variance?
