Part -1
Make sure you read the output carefully. This output pertains to a set of juvenile court data looking at the length of time that juvenile offenders are held in secure detention while their case is being processed through juvenile court. For this regression model, the following variables are used:
LOS: the length of stay in detention, in days
Number of filed charges: the number of different crimes they are currently charged with
Number of prior JD/JS cases: the number of prior juvenile court cases
Number of prior felonies: the number of prior charges for felonies
offlevel: this measure indicates the severity of the most serious charge they are charged with, where 0 is for the least severe and 8 is for the most severe
female: a dummy variable coded 0 for males and 1 for females
black: a dummy variable coded 1 for blacks
otherrac: a dummy variable coded 1 for the "other race" category (Note that when black and other race are in the model together, then the 0 category on each variable refers to whites)
The following questions pertain to the data:
a) What is the equation for this regression model?
b) Write one sentence describing what we have learned about the relationship between the dependent variable and each of the independent variables found to have a statistically significant relationship on the dependent variable. Write a sentence for each relationship. Be specific.
c) What can you conclude about the fit of the model? Explain.
d) What concerns, if any, can you raise about the model, based on the information provided here on the output? Explain.
Regression
Descriptive Statistics
|
|
Mean
|
Std. Deviation
|
N
|
|
LOS
Number of filed charges
Number of prior JD/JS
cases
Number of prior felonies otherrac
black female offlevel
|
11.84
2.25
3.72
.83
.0861
.5976
.2490
3.4211
|
20.098
1.897
2.843
1.196
.28051
.49046
.43251
1.25469
|
2719
2719
2719
2719
2719
2719
2719
2719
|
|
|
LOS
|
Number of filed charges
|
Number of prior JD/JS cases
|
Number of prior felonies
|
|
Pearson Correlation LOS
Number of filed charges
Number of prior JD/JS
cases
Number of prior felonies otherrac
black female offlevel
|
1.000
.116
.294
.266
.035
.061
-.084
.161
|
.116
1.000
.040
.030
.010
.035
-.108
.248
|
.294
.040
1.000
.665
-.025
.162
-.143
-.024
|
.266
.030
.665
1.000
-.023
.131
-.208
.061
|
|
Sig. (1-tailed) LOS
Number of filed charges
Number of prior JD/JS
cases
Number of prior felonies otherrac
black female offlevel
|
.
.000
.000
.000
.034
.001
.000
.000
|
.000
.
.018
.060
.303
.033
.000
.000
|
.000
.018
.
.000
.095
.000
.000
.106
|
.000
.060
.000
.
.117
.000
.000
.001
|
|
N LOS
Number of filed charges
Number of prior JD/JS
cases
Number of prior felonies otherrac
black female offlevel
|
2719
2719
2719
2719
2719
2719
2719
2719
|
2719
2719
2719
2719
2719
2719
2719
2719
|
2719
2719
2719
2719
2719
2719
2719
2719
|
2719
2719
2719
2719
2719
2719
2719
2719
|
Correlations
|
|
otherrac
|
black
|
female
|
offlevel
|
|
Pearson Correlation LOS
Number of filed charges
Number of prior JD/JS
cases
Number of prior felonies otherrac
black female offlevel
|
.035
.010
-.025
-.023
1.000
-.374
-.071
-.047
|
.061
.035
.162
.131
-.374
1.000
-.027
.072
|
-.084
-.108
-.143
-.208
-.071
-.027
1.000
-.174
|
.161
.248
-.024
.061
-.047
.072
-.174
1.000
|
|
Sig. (1-tailed) LOS
Number of filed charges
Number of prior JD/JS
cases
Number of prior felonies otherrac
black female offlevel
|
.034
.303
.095
.117
.
.000
.000
.008
|
.001
.033
.000
.000
.000
.
.079
.000
|
.000
.000
.000
.000
.000
.079
.
.000
|
.000
.000
.106
.001
.008
.000
.000
.
|
|
N LOS
Number of filed charges
Number of prior JD/JS
cases
Number of prior felonies otherrac
black female offlevel
|
2719
2719
2719
2719
2719
2719
2719
2719
|
2719
2719
2719
2719
2719
2719
2719
2719
|
2719
2719
2719
2719
2719
2719
2719
2719
|
2719
2719
2719
2719
2719
2719
2719
2719
|
Model Summaryb
|
Model
|
R
|
R Square
|
Adjusted R Square
|
Std. Error of the Estimate
|
|
1
|
.358a
|
.128
|
.126
|
18.794
|
a. Predictors: (Constant), offlevel, Number of prior JD/JS cases, otherrac, female, Number of filed charges, black, Number of prior felonies
b. Dependent Variable: LOS
ANOVAb
|
Model
|
Sum of
Squares
|
df
|
Mean Square
|
F
|
Sig.
|
|
1 Regression
Residual
Total
|
140415.78
957518.90
1097934.7
|
7
2711
2718
|
20059.397
353.198
|
56.794
|
.000a
|
a. Predictors: (Constant), offlevel, Number of prior JD/JS cases, otherrac, female, Number of filed charges, black, Number of prior felonies
b. Dependent Variable: LOS
Coefficientsa
|
Model
|
Unstandardized
Coefficients
|
Standardized
Coefficients
|
t
|
Sig.
|
|
B
|
Std. Error
|
Beta
|
|
1 (Constant)
Number of filed charges
Number of prior JD/JS
cases
Number of prior felonies otherrac
black female offlevel
|
-5.976
.714
1.575
1.808
4.085
.794
.335
2.325
|
1.343
.197
.172
.410
1.393
.806
.869
.303
|
.067
.223
.108
.057
.019
.007
.145
|
-4.449
3.626
9.170
4.407
2.933
.986
.385
7.683
|
.000
.000
.000
.000
.003
.324
.700
.000
|
a. Dependent Variable: LOS
Residuals Statisticsa
|
|
Minimum
|
Maximum
|
Mean
|
Std. Deviation
|
N
|
|
Predicted Value
Residual
Std. Predicted Value
Std. Residual
|
-5.64
-35.960
-2.432
-1.913
|
47.67
252.596
4.984
13.441
|
11.84
.000
.000
.000
|
7.188
18.769
1.000
.999
|
2719
2719
2719
2719
|
a. Dependent Variable: LOS
Part-2
Pay equity for men and women has been an ongoing source of conflict for a number of years in North America. Suppose that a statistics practitioner is investigating the factors that affect salary differences between male and female university professors. He believes that the following variables have some impact on a professor's salary:
Number of years since first degree (years)
Highest degree, coded 1 for Ph.D and 0 otherwise (phd)
Average score on teaching evaluations (evaluati)
Number of articles published (articles)
Gender, coded 1 if male and 0 if female (gender)
The following questions pertain to the data:
a) What is the equation for this regression model?
b) Write one sentence describing what we have learned about the relationship between the dependent variable and each of the independent variables found to have a statistically significant relationship on the dependent variable. Write a sentence for each relationship. Be specific.
c) What can you conclude about the fit of the model? Explain.
d) What concerns can you raise about the model, based on the information provided here on the output? Explain.
Regression
Descriptive Statistics
|
|
Mean
|
Std. Deviation
|
N
|
|
salary
|
44889.790
|
12906.32702
|
100
|
|
years
|
23.7000
|
9.54151
|
100
|
|
phd
|
.8500
|
.35887
|
100
|
|
evaluati
|
5.3496
|
.54142
|
100
|
|
articles
|
12.1600
|
5.92839
|
100
|
|
gender
|
.6300
|
.48524
|
100
|
Correlations
|
|
salary
|
years
|
phd
|
evaluati
|
articles
|
gender
|
|
Pearson Correlation
|
salary
|
1.000
|
.941
|
-.030
|
.475
|
.798
|
.070
|
|
|
years
|
.941
|
1.000
|
-.161
|
.304
|
.698
|
.009
|
|
|
phd
|
-.030
|
-.161
|
1.000
|
.176
|
.187
|
.142
|
|
|
evaluati
|
.475
|
.304
|
.176
|
1.000
|
.409
|
.074
|
|
|
articles
|
.798
|
.698
|
.187
|
.409
|
1.000
|
.038
|
|
|
gender
|
.070
|
.009
|
.142
|
.074
|
.038
|
1.000
|
|
Sig. (1-tailed)
|
salary
|
.
|
.000
|
.383
|
.000
|
.000
|
.246
|
|
|
years
|
.000
|
.
|
.055
|
.001
|
.000
|
.467
|
|
|
phd
|
.383
|
.055
|
.
|
.040
|
.031
|
.079
|
|
|
evaluati
|
.000
|
.001
|
.040
|
.
|
.000
|
.233
|
|
|
articles
|
.000
|
.000
|
.031
|
.000
|
.
|
.352
|
|
|
gender
|
.246
|
.467
|
.079
|
.233
|
.352
|
.
|
|
N
|
salary
|
100
|
100
|
100
|
100
|
100
|
100
|
|
|
years
|
100
|
100
|
100
|
100
|
100
|
100
|
|
|
phd
|
100
|
100
|
100
|
100
|
100
|
100
|
|
|
evaluati
|
100
|
100
|
100
|
100
|
100
|
100
|
|
|
articles
|
100
|
100
|
100
|
100
|
100
|
100
|
|
|
gender
|
100
|
100
|
100
|
100
|
100
|
100
|
Model Summary
|
Model
|
R
|
R Square
|
Adjusted R Square
|
Std. Error of the Estimate
|
|
1
|
.974a
|
.948
|
.945
|
3014.94701
|
a. Predictors: (Constant), gender, years, phd, evaluati, articles
b. Dependent Variable: salary
ANOVAb
|
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
|
1
|
Regression
|
1.6E+010
|
5
|
3127260664
|
344.037
|
.000a
|
|
|
Residual
|
8.5E+008
|
94
|
9089905.455
|
|
|
Total
|
1.6E+010
|
99
|
a. Predictors: (Constant), gender, years, phd, evaluati, articles
b. Dependent Variable: salary
Coefficientsa
|
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
|
B
|
Std. Error
|
Beta
|
|
1
|
(Constant)
|
-5916.189
|
3140.847
|
.755
|
-1.884
|
.063
|
|
|
years
|
1021.696
|
48.926
|
20.883
|
.000
|
|
|
phd
|
725.748
|
961.524
|
.020
|
.755
|
.452
|
|
|
evaluati
|
3728.939
|
619.822
|
.156
|
6.016
|
.000
|
|
|
articles
|
439.148
|
80.693
|
.202
|
5.442
|
.000
|
|
|
gender
|
1089.720
|
631.980
|
.041
|
1.724
|
.088
|
a. Dependent Variable: salary
Residuals Statisticsa
|
|
Minimum
|
Maximum
|
Mean
|
Std. Deviation
|
N
|
|
Predicted Value
|
21557.234
|
68157.203
|
44889.790
|
12567.51597
|
100
|
|
Residual
|
-7197.878
|
7003.2856
|
.00000
|
2937.82561
|
100
|
|
Std. Predicted Value
|
-1.857
|
1.851
|
.000
|
1.000
|
100
|
|
Std. Residual
|
-2.387
|
2.323
|
.000
|
.974
|
100
|
a. Dependent Variable: salary