Please go into detail about how you solved! Thankyou A researcher studying Total
ID: 3134496 • Letter: P
Question
Please go into detail about how you solved! Thankyou
A researcher studying Total Serious Crimes (TSC) obtained a data set from the U.S. Bureau of Census (see the Minitab data file named TSC.mtw). The data set provides information for 109 Standard Metropolitan Statistical Areas (SMSAs) in the United States. The data set contains five variables: TP, PPCC, PP65, PH, and TPI. Descriptions of the variables can be found in the table below. The researcher believes that all these five variables can be used to predict TSC. 14 points
Variable
Definition
Description
TP
Total population
Estimated population (in thousands)
PPCC
Percent of population in central cities
Percent of SMSA population in central city or cities.
PP65
Percent of population 65 or older
Percent of SMSA population 65 years old or older
PH
Percent high school graduates
Percent of adult population who completed 12 or more years of school
TPI
Total personal income
Total current income received by residents of the SMSA from all sources (in millions of dollars)
TSC
Total serious crimes
Total number of serious crimes
Perform a regression analysis. Report the initial model. 2 points
Does the initial model contain insignificant predictors? What are the two main reasons why a model contains insignificant predictors? 3 points
Is the initial model plagued with multi-collinearity? How do you know? 3 points
How would you deal with the multi-collinearity issue? 2 points
After dealing with the multi-collinearity issue, are the remaining predictors all significant? 1 point
What is your final regression model? 3 points
Variable
Definition
Description
TP
Total population
Estimated population (in thousands)
PPCC
Percent of population in central cities
Percent of SMSA population in central city or cities.
PP65
Percent of population 65 or older
Percent of SMSA population 65 years old or older
PH
Percent high school graduates
Percent of adult population who completed 12 or more years of school
TPI
Total personal income
Total current income received by residents of the SMSA from all sources (in millions of dollars)
TSC
Total serious crimes
Total number of serious crimes
Explanation / Answer
From Minitab Using the following path we get the data as below.
Stat-Regression-Regression
The regression equation is
TP = 154 + 0.360 PPCC - 0.79 PP65 - 2.32 PH + 0.127 TPI + 0.00236 TSC
Predictor Coef SE Coef T P
Constant 153.79 37.79 4.07 0.000
PPCC 0.3597 0.2158 1.67 0.099
PP65 -0.785 2.294 -0.34 0.733
PH -2.3225 0.4673 -4.97 0.000
TPI 0.127202 0.005979 21.27 0.000
TSC 0.0023648 0.0006170 3.83 0.000
the initial model contain insignificant predictors
P value for PPCC and PP65 is higher than 0.05 hence at 5% level of significance we can say that we can
remove PPCC and PP65 from our model
Also here R-Sq(adj) = 97.4%
Now leaving the two variables the predicted model is
The regression equation is
TP = 155 - 2.20 PH + 0.124 TPI + 0.00273 TSC
Predictor Coef SE Coef T P
Constant 154.87 25.89 5.98 0.000
PH -2.1958 0.4624 -4.75 0.000
TPI 0.124133 0.005436 22.83 0.000
TSC 0.0027304 0.0005510 4.96 0.000
From the p value we can say that after dealing with the multi-collinearity issue, the remaining predictors all significant.
R-Sq(adj) = 97.4%
hence there is no change in adjusted R square
R square defines the percentage of variation in the response reflected by the model.