Incarceration rates vary from state to state.We must remember that correlation i
ID: 3155393 • Letter: I
Question
Incarceration rates vary from state to state.We must remember that correlation is not causation but we can ask: “what state level factors might be associated with the state incarceration rate?
I drew a sample of 17 states using a systematic random sampling method (Chapter 7). Using data from the Bureau of Justice Statistics, the Kaiser Foundation and the FBI, I gathered published data on:
Incarceration Rate per 100,000 Adults (2013)
Median State Income (2010-2013)
Total Crime Rate from Uniform Crime Reports (Violent crime and Property crime)
Before you look at the data (on the next page), state an appropriate null and research hypothesis concerning the relationship between Incarceration Rate and each of the two independent variables.
Which of these predicted relationships do you expect to be strongest?Why?
For each of these relationships, calculate:
The prediction equation (least squares line)
The Coefficient of Determination
Pearson’s r
Would multiple regression be a useful statistical tool for further analysis of these data?Why or why not?You do not need to do any calculations.
Incarceration Rate
Median
Violent Crime
Prop crime
Total crime
per 100,00 Adults
Income
Rate
Rate
Rate
2013
2010-2013
2012
2012
2012
State
Alabama
910
43330
449.9
3502.2
3952.1
Arkansas
1010
40877
469.1
3660.1
4129.2
Connecticut
620
67807
283
2140
2423
Florida
990
47106
487.1
3276.7
3763.8
Idaho
860
49952
207.9
1983.5
2191.4
Iowa
530
53364
263.9
2271.8
2535.7
Louisiana
1420
40844
496.9
3540.6
4037.5
Massachusetts
400
64555
405.5
2153
2558.5
Mississippi
950
40338
260.8
2811
3071.8
Nebraska
600
55107
259.4
2754.9
3014.3
New Jersey
540
65321
290.2
2047.3
2337.5
North Carolina
730
44254
353.4
3369.5
3722.9
Oklahoma
740
47282
469.3
3401
3870.3
Rhode Island
400
55158
252.4
2572.3
2824.7
Tennessee
960
42785
643.6
3371.4
4015
Vermont
410
56175
142.6
2398.7
2541.3
West Virginia
660
43361
316.3
2364.9
2681.2
Mean
748.82
50448.00
355.96
2801.11
3157.07
SD
273.52
9056.11
130.62
601.63
703.41
Incarceration Rate
Median
Violent Crime
Prop crime
Total crime
per 100,00 Adults
Income
Rate
Rate
Rate
2013
2010-2013
2012
2012
2012
State
Alabama
910
43330
449.9
3502.2
3952.1
Arkansas
1010
40877
469.1
3660.1
4129.2
Connecticut
620
67807
283
2140
2423
Florida
990
47106
487.1
3276.7
3763.8
Idaho
860
49952
207.9
1983.5
2191.4
Iowa
530
53364
263.9
2271.8
2535.7
Louisiana
1420
40844
496.9
3540.6
4037.5
Massachusetts
400
64555
405.5
2153
2558.5
Mississippi
950
40338
260.8
2811
3071.8
Nebraska
600
55107
259.4
2754.9
3014.3
New Jersey
540
65321
290.2
2047.3
2337.5
North Carolina
730
44254
353.4
3369.5
3722.9
Oklahoma
740
47282
469.3
3401
3870.3
Rhode Island
400
55158
252.4
2572.3
2824.7
Tennessee
960
42785
643.6
3371.4
4015
Vermont
410
56175
142.6
2398.7
2541.3
West Virginia
660
43361
316.3
2364.9
2681.2
Mean
748.82
50448.00
355.96
2801.11
3157.07
SD
273.52
9056.11
130.62
601.63
703.41
Explanation / Answer
Incarceration Rate vs median income and Violent Crime Regression Statistics Multiple R 0.686539 R Square 0.471336 Adjusted R Square 0.405253 Standard Error 215.9203 Observations 19 ANOVA df SS MS F Significance F Regression 2 665054.6 332527.3 7.13248 0.006102 Residual 16 745944.9 46621.56 Total 18 1411000 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 415.0107 237.713 1.745848 0.100006 -88.9184 918.9397 X Variable 1 -0.00358 0.003985 -0.8972 0.382913 -0.01202 0.004873 X Variable 2 1.398994 0.381056 3.67136 0.002063 0.591191 2.206797 Incarceration Rate vs Prop crime and Violent Crime Regression Statistics Multiple R 0.750632 R Square 0.563449 Adjusted R Square 0.50888 Standard Error 196.21 Observations 19 ANOVA df SS MS F Significance F Regression 2 795025.9 397513 10.32545 0.001319 Residual 16 615973.6 38498.35 Total 18 1411000 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 8.177256 169.9133 0.048126 0.962211 -352.023 368.3774 X Variable 1 0.540953 0.537336 1.00673 0.329048 -0.59815 1.680055 X Variable 2 0.197177 0.09453 2.085868 0.05336 -0.00322 0.397571