Please verify my answers. Especially my variables on each axis in the scatterplot. Thanks!

Q2. Test a hypothesis with bivariate regression.(11 points)

Suppose a researcher wishes to use the same data set from Q1 to answer the following question:

Can the average number of years adults have spent in schooling in a state significantly predict crime rate in that state?

A. What is the null hypothesis being tested for this research question?

H0: The average number of years adults have spent in schooling in a state does not significantly predict the crime rate in that state.

Or ?

H0: There is no significant relationship between the average number of years adults have spent in schooling and the crime rate in a state.

B. Show a scatterplot with the outcome variable on the Y-axis. (Note: In SPSS, select "Legacy Dialogs" at the bottom of the "Graphs" menu. Choose "Scatter/Dot" and "Simple Scatter.") [Paste the scatterplot here.]

C. Examine the scatterplot. Is there a hint of a linear relationship? How do you know?

The scatterplot shows a negative linear relationship between education and crime rates. As education increases, crime rates decrease, which suggests that the more years adults spend in school, the less likely they are to commit a crime.

Below is the SPSS output table for a test of the regression model (omnibus test).Use the information in this table to answer the questions in D and E.

Model Summaryb
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate	Change Statistics
R Square Change	F Change	df1	df2	Sig. F Change
1	.531a	.282	.266	33.5409	.282	17.645s	1	45	<.001
a. Predictors: (Constant), Education
b. Dependent Variable: CrimeRate

D. Is theregression model statistically significant? Explain your answer. In other words, what does statistical significance or non-significance mean in this context?

Yes, the regression model is statistically significant. The significance (p-value) = <0.001, which is less than 0.05. In this context, the statistical significance means that we can reject the null hypothesis and state that the coefficient is statistically different from zero.

E. How much of the variance in the outcome variable is accounted for by the predictor variable in this model?

The variance in the outcome variable accounted for by the predictor variable in this model is 26..6% (Adjusted R Square = 0.266).

OR

Is it ( 0.282 = R square Change) = 28.2% ???

Below is the output table for the coefficients. Use the information in this table to answer the questions in F - I.

Coefficientsa
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.
B	Std. Error	Beta
1	(Constant)	298.627	47.053		6.347	<.001
Education	-17.286	4.115	-.531	-4.201	<.001
a. Dependent Variable: CrimeRate

F. What is the linear equation (i.e., the equation for the prediction line) formed by the unstandardized coefficients?

= a + bx

CrimeRate: = 298.627-17.286x (Education)

Constant: 298.627: Slope: 17.286: Predictor variable: Education

G. What is the standardized coefficient for the predictor variable?

-.531

H. Should the researcherreject orfail to reject the hypothesis? Explain how you arrived at your answer.

Since the p-value of <.001 is less than 0.05, the researcher should reject the null hypothesis. This indicates that there is a statistically significant relationship between the predictor and the outcome variable.Moreover, the T value for schooling is -4.201, indicating a statistically significant result. The likelihood of randomly observing such a significant correlation between education and crime rate is exceedingly small. Thus, the researcher can reject the null hypothesis that there is no relationship between education and crime rate. Contrary to the null hypothesis, the data suggests that as education increases, crime rates decrease (negative correlation between education levels and crime rates).

I. Complete the table. States 48, 49, and 50 have the average schooling in years (Education) as listed below in the table. Use the linear equation found in (F) to estimate the crime rate in those states. You must show your work (the values placed into the equation to make the prediction).

State	Education	Prediction Equation	Estimated Crime Rate
48	12.2	=298.627-17.286*12.2	87.7378
49	11.5	=298.627-17.286*11.5	99.838
50	13.8	=298.627-17.286*13.8	60.0802