Researchers analyzed relationships between crime rate at the county level and ot
ID: 3325024 • Letter: R
Question
Researchers analyzed relationships between crime rate at the county level and other county level variables for 25 counties in Florida. Crime rate was measured as the number of crimes in that county in the past year per 1000 residents, urbanization was measured as the percentage of residents who live in metropolitan areas, and education was measured as the percentage of residents aged at least 25 in the county who had a least a high school degree. The output below shows two estimated linear regression equations used to predict crime rates, the first with education as the independent variable and the second with urbanization as the dependent variable.
Figure 1: Regression with y = crime rate as number of crimes per 1000 residents, and x = % with high school degree
Regression Statistics
R Square
0.1813
Adjusted R Square
0.1457
Standard Error
24.49
Observations
25
Coefficients
Standard Error
t Stat
P-value
Intercept
-28.47
35.03
-0.81
0.4247
education
1.15
0.51
2.26
0.0338
Figure 2: Regression with y = crime rate as number of crimes per 1000 residents, and x = % urbanization
Regression Statistics
R Square
0.3906
Adjusted R Square
0.3641
Standard Error
21.13
Observations
25
Coefficients
Standard Error
t Stat
P-value
Intercept
27.95
7.09
3.94
0.0006
urbanization
0.48
0.13
3.84
0.0008
Now examine the output in Figure 2.
1.) What are the null and alternative hypotheses tested on the line with a p-value of 0.0006?
Ho: 1_hat = 0 vs Ha: 1_hat 0
2) Which model, the one with % urbanization or % education as the independent variable, is better at predicting crime rate?
Regression Statistics
R Square
0.1813
Adjusted R Square
0.1457
Standard Error
24.49
Observations
25
Explanation / Answer
The p-value here is given to be p = 0.0006
It is the p-value for the significance of the intercept in the regression equation.
Therefore the null and the alternate hypothesis for the significance of intercept is given here as:
Ho: o = 0 vs Ha: o 0
Therefore B is the correct answer here.
Question 2:
The R2 and the adjusted R2 values here for the second model % urbanization is more than the one with the first model that is with % education , therefore the one with the % urbanization is is better at predicting crime rate
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