Crime Rates. These data are crime-related and demographic statistics for 47 US states in 1960. The data were collected ...

Crime Rates. These data are crime-related and demographic statistics for 47 US states in 1960. The data were collected from the FBI's Uniform Crime Report and other government agencies to determine how the variable crime rate depends on the other variables measured in the study. There have been hypotheses that the amount spent on the police force and unemployment rates could be indicators of crime. Scatterplots of the two potential independent variables appear below.

Variables are:

R: Crime rate: # of offenses reported to police per million population

Ex0: 1960 per capita expenditure on police by state and local government

U2: Unemployment rate of urban males per 1000 of age 35-39

a. Does there seem to be a strong linear relationship between either Crime (R) and amount spent on police (Ex0) or Unemployment Rate (U2)? Explain the relationship (if any) that you see between R and each of the independent variables. If you had to choose one of the X variables to predict R, which one would you choose?

Regression Analysis: R versus Ex0

The regression equation is

Predictor Coef SE Coef T P

Constant 14.45 12.67 1.14 0.260

Ex0 0.8948 0.1409 6.35 0.000

S = R-Sq = 47.3% R-Sq(adj) = 46.1%

Analysis of Variance

Source DF SS MS F P

Regression 1 32533 32533 40.36 0.000

Residual Error 45 36276 806

Total 46 68809

Regression Analysis: R versus U2

The regression equation is

Predictor Coef SE Coef T P

Constant 62.92 23.51 2.68 0.010

U2 0.8120 0.6719 1.21 0.233

S = R-Sq = 3.1% R-Sq(adj) = 1.0%

Analysis of Variance

Source DF SS MS F P

Regression 1 2164 2164 1.46 0.233

Residual Error 45 66646 1481

Total 46 68809

b. Using whichever variable you chose above, write out the regression equation (outputs can be found above). Interpret both coefficients.

c. Is your chosen variable statistically significant or useful? Prove your answer.

d. Using only your chosen variable, utilize the regression equation to predict the Crime Rate for an area that has an Unemployment Rate of 40 and spends $100 per capita on the police force.

e. What is the value for the standard error of estimate?

f. Create a confidence interval for the slope of your regression equation. Is it plausible that the true slope may actually be equal to one? Why?

g. Use only your chosen variable’s output and predict the crime rate for a value of 50 in your variable

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