Homework SourseE State whether you think there is a relationship between th
E. State whether you think there is a relationship between the two variables, and justify your answer.
F. We know that the percentage of urban population in Idaho is 35%. We also know that the percentage of urban population in Florida is 78%. Predict the robbery rates in each of thesestates. Are these extrapolations or interpolation, and are they valid predictions?
Solution
let assume that the regression model is
RR=b0+b1UP
RR=Robbery rate
UP=urban population
b0 and b1 are the parameters
E.
Yes there is a positive correlation between two variable because the R2 is tends to one.
F. The regression equation is
RR=-117.031+376.7456UP
For Idaho is 35% then
RR=-117.031+376.7456*0.35=14.8299
For Florida is 78%
RR=117.031+376.7456*0.78=176.83
They are valid predictions.
| SUMMARY OUTPUT | ||||||
| Regression Statistics | ||||||
| Multiple R | 0.820521 | |||||
| R Square | 0.673255 | |||||
| Adjusted R Square | 0.632412 | |||||
| Standard Error | 57.62848 | |||||
| Observations | 10 | |||||
| ANOVA | ||||||
| df | SS | MS | F | Significance F | ||
| Regression | 1 | 54743.77 | 54743.77 | 16.48392 | 0.003633 | |
| Residual | 8 | 26568.33 | 3321.041 | |||
| Total | 9 | 81312.1 | ||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | -117.031 | 66.65978 | -1.75565 | 0.117221 | -270.749 | 36.68653 |
| X Variable 1 | 376.7456 | 92.79359 | 4.060039 | 0.003633 | 162.7632 | 590.728 |
