Please verify my answers.

Q2. Test a hypothesis with bivariate regression.

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: Crime Rate

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

CODE BOOK

Variable	Description	Values
Q1Q2
CrimeRate	Number of offences per million people	Crime count
Education	Average number of years of schooling	number of years
Expenditure	Police expenditure per capita on police (in thousands)	number of thousands
YouthUnemploy	Number of males unemployed aged 18-24 per 1000	number of people
MatureUnemploy	Number of males unemployed aged 25-39 per 1000	number of people
BelowWage	Poverty rate; Number of families below half the average wage per 1000	number of families
CrimeRate Category	Classification of crime by crime rate	LOW CRIME	crime rate of 0 - 76.6	1
		LOW AVERAGE CRIME	crime rate of 76.6 - 103.5	2
		HIGH AVERAGE CRIME	crime rate of 103.6 - 130.3	3
		HIGH CRIME	crime rate130.4 - 179.2	4
DomPolit	Dominant Political Party: The majority of the populace in the state voted for the specified party in all major elections over the past 2 years.	DEM	democratic	1
		REP	republican	2

DATA SET

State	CrimeRate	Education	Expenditure	YouthUnemploy	MatureUnemploy	BelowWage	CrimeRate Category	DomPolit
1	26.5	11.1	75	80	21	123	LOW CRIME	DEM
2	36.9	12.9	54	136	39	210	LOW CRIME	REP
3	37.1	12.2	44	98	33	256	LOW CRIME	REP
4	42.7	10.8	41	101	50	235	LOW CRIME	DEM
5	45.7	11.2	97	79	24	162	LOW CRIME	DEM
6	47.9	12.8	60	81	24	199	LOW CRIME	DEM
7	50.6	13.1	57	71	29	176	LOW CRIME	REP
8	52.9	12	63	119	21	168	LOW CRIME	REP
9	61.8	14.1	54	110	22	126	LOW CRIME	DEM
10	69.4	12.2	47	97	28	215	LOW CRIME	REP
11	72.4	12.1	44	93	36	247	LOW CRIME	DEM
12	75.4	13.4	87	112	34	146	LOW CRIME	REP
13	77.3	12.7	61	95	28	189	LOW AVERAGE CRIME	REP
14	79.6	12.3	115	82	33	127	LOW AVERAGE CRIME	DEM
15	80.6	11.2	54	76	25	246	LOW AVERAGE CRIME	DEM
16	82.2	11.9	68	104	25	213	LOW AVERAGE CRIME	REP
17	87.5	12.9	67	107	34	199	LOW AVERAGE CRIME	REP
18	92.9	13	128	80	39	140	LOW AVERAGE CRIME	REP
19	94.1	10.9	81	106	35	162	LOW AVERAGE CRIME	REP
20	95.2	10.1	56	110	36	254	LOW AVERAGE CRIME	DEM
21	97.8	12	53	92	41	243	LOW AVERAGE CRIME	DEM
22	99.9	11	70	80	28	321	LOW AVERAGE CRIME	REP
23	102.4	10.5	54	84	32	249	LOW AVERAGE CRIME	REP
24	103.5	11.9	56	79	28	257	LOW AVERAGE CRIME	REP
25	104.5	11.7	71	87	28	182	HIGH AVERAGE CRIME	DEM
26	105.4	10.4	91	119	41	159	HIGH AVERAGE CRIME	REP
27	107.8	10.2	62	99	29	243	HIGH AVERAGE CRIME	DEM
28	110.1	12.9	66	87	45	151	HIGH AVERAGE CRIME	REP
29	111.5	10.8	97	103	34	160	HIGH AVERAGE CRIME	DEM
30	113.5	11.3	115	93	35	175	HIGH AVERAGE CRIME	DEM
31	116.3	10.7	77	117	51	256	HIGH AVERAGE CRIME	DEM
32	118.7	10.9	79	99	43	170	HIGH AVERAGE CRIME	REP
33	124.5	8.1	73	143	41	177	HIGH AVERAGE CRIME	DEM
34	127.8	11	96	115	36	132	HIGH AVERAGE CRIME	REP
35	129.8	10.9	157	93	47	169	HIGH AVERAGE CRIME	DEM
36	130.7	10	64	73	60	220	HIGH CRIME	DEM
37	133.5	10.8	74	89	36	230	HIGH CRIME	REP
38	134.6	9.9	83	83	56	234	HIGH CRIME	DEM
39	137.5	9.8	76	120	41	204	HIGH CRIME	DEM
40	140.5	11.5	105	131	61	174	HIGH CRIME	DEM
41	142.7	10.2	101	94	58	180	HIGH CRIME	DEM
42	152.6	13	98	88	38	151	HIGH CRIME	REP
43	157.3	10.1	109	82	50	312	HIGH CRIME	REP
44	162.7	11	95	97	45	196	HIGH CRIME	DEM
45	165.6	11	116	79	42	172	HIGH CRIME	DEM
46	177.2	9.8	141	110	60	169	HIGH CRIME	REP
47	179.2	10.2	143	190	67	150	HIGH CRIME	DEM