Correlation and Regression with SPSS

The purpose of this paper is to state the assumptions for the Pearson correlation coefficient and a simple linear regression, develop null and alternative hypotheses, determine whether to reject or retain the null hypothesis, report on the SPSS analysis, generate a scatterplot and syntax and output files in SPSS.

Statistical Assumptions
The two statistical assumptions of the Pearson correlation are that the variables are bivariately normally distributed, the cases represent randomly selected samples from the population, and scores on variables for one case are independent of scores on these variables for other cases (Green & Salkind, 2014).

Brief Analysis

The research question is: Does age and the number of hours worked last week relate in a statistically significant linear fashion?

The null hypothesis is: Ho: ρ= 0; There is no correlation between the variables.

The alternative hypothesis is: H1: ρ ≠ 0; there is a real correlation between the variables.

The independent variable is age and the dependent variable is hours worked last week. Correlation coefficients were computed among the two continuous variables of age and hours worked last week. To control for Type 1 error across the two correlations, I utilized the Bonferroni approach to calculate a p value of less than .025 (.05/2 = .025) was required for significance. The results in the table 1 shows that both correlations were statistically significant at the .01 level of significance. I found r(1483) = .32, p > .000. There is a significant negative relationship between the age of participants and the number of hours worked last week. I reject the null hypothesis. The effect size is .1

A linear regression analysis was conducted to evaluate the prediction of age as it affects hours worked last week. The scatter plot for the two variables, as shown in Figure 1 indicates that the two variables are linearly related such that as age increases, the number of hours worked last week decreases.



Syntax and Output Files

Notes
Output Created		01-FEB-2014 09:14:02
Comments
Input	Data	C:\Users\Deborah\Desktop\Stats\gss04student_corrrected.sav
	Active Dataset	DataSet1
	Filter	<none>
	Weight	<none>
	Split File	<none>
	N of Rows in Working Data File	1500
Missing Value Handling	Definition of Missing	User-defined missing values are treated as missing.
	Cases Used	Statistics are based on all cases with valid data for all variables in the model.
Syntax		UNIANOVA INCOME BY RACE   /METHOD=SSTYPE(3)   /INTERCEPT=INCLUDE   /POSTHOC=RACE(TUKEY QREGW C)   /EMMEANS=TABLES(RACE)   /PRINT=ETASQ HOMOGENEITY DESCRIPTIVE   /CRITERIA=ALPHA(.05)   /DESIGN=RACE.
Resources	Processor Time	00:00:00.08
	Elapsed Time	00:00:00.08

Correlations

CORRELATIONS

  /VARIABLES=AGE HRS1

  /PRINT=TWOTAIL NOSIG

  /STATISTICS DESCRIPTIVES

  /MISSING=PAIRWISE.

Descriptive Statistics
		Mean	Std. Deviation	N
AGE OF RESPONDENT		46.22	16.679	1495
NUMBER OF HOURS WORKED LAST WEEK		26.94	23.570	1490

Table 1.

Correlations
		AGE OF RESPONDENT	NUMBER OF HOURS WORKED LAST WEEK
AGE OF RESPONDENT	Pearson Correlation	1	-.325**
	Sig. (2-tailed)		.000
	N	1495	1485
NUMBER OF HOURS WORKED LAST WEEK	Pearson Correlation	-.325**	1
	Sig. (2-tailed)	.000
	N	1485	1490
**. Correlation is significant at the 0.01 level (2-tailed).

GRAPH

  /SCATTERPLOT(MATRIX)=AGE HRS1

  /MISSING=LISTWISE.

Graph

 [DataSet1] C:\Users\Deborah\Desktop\Stats\gss04student_corrrected.sav

GET

  FILE='C:\Users\Deborah\Desktop\Stats\gss04student_corrrected.sav'.

DATASET NAME DataSet1 WINDOW=FRONT.

CORRELATIONS

  /VARIABLES=AGE HRS1

  /PRINT=TWOTAIL NOSIG

  /STATISTICS DESCRIPTIVES

  /MISSING=PAIRWISE.

Correlations

Notes
Descriptive Statistics
	Mean	Std. Deviation	N
AGE OF RESPONDENT	46.22	16.679	1495
NUMBER OF HOURS WORKED LAST WEEK	26.94	23.570	1490

Correlations
		AGE OF RESPONDENT	NUMBER OF HOURS WORKED LAST WEEK
AGE OF RESPONDENT	Pearson Correlation	1	-.325**
	Sig. (2-tailed)		.000
	N	1495	1485
NUMBER OF HOURS WORKED LAST WEEK	Pearson Correlation	-.325**	1
	Sig. (2-tailed)	.000
	N	1485	1490
**. Correlation is significant at the 0.01 level (2-tailed).

REGRESSION

  /DESCRIPTIVES MEAN STDDEV CORR SIG N

  /MISSING LISTWISE

  /STATISTICS COEFF OUTS CI(95) R ANOVA

  /CRITERIA=PIN(.05) POUT(.10)

  /NOORIGIN

  /DEPENDENT HRS1

  /METHOD=ENTER AGE.

Regression

Descriptive Statistics
	Mean	Std. Deviation	N
NUMBER OF HOURS WORKED LAST WEEK	26.97	23.572	1485
AGE OF RESPONDENT	46.22	16.697	1485

Correlations
		NUMBER OF HOURS WORKED LAST WEEK	AGE OF RESPONDENT
Pearson Correlation	NUMBER OF HOURS WORKED LAST WEEK	1.000	-.325
	AGE OF RESPONDENT	-.325	1.000
Sig. (1-tailed)	NUMBER OF HOURS WORKED LAST WEEK	.	.000
	AGE OF RESPONDENT	.000	.
N	NUMBER OF HOURS WORKED LAST WEEK	1485	1485
	AGE OF RESPONDENT	1485	1485

Variables Entered/Removeda
Model	Variables Entered	Variables Removed	Method
1	AGE OF RESPONDENTb	.	Enter
a. Dependent Variable: NUMBER OF HOURS WORKED LAST WEEK
b. All requested variables entered.

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.325a	.105	.105	22.302
a. Predictors: (Constant), AGE OF RESPONDENT

ANOVAa
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	86941.814	1	86941.814	174.798	.000b
	Residual	737619.214	1483	497.383
	Total	824561.028	1484
a. Dependent Variable: NUMBER OF HOURS WORKED LAST WEEK
b. Predictors: (Constant), AGE OF RESPONDENT

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.	95.0% Confidence Interval for B
		B	Std. Error	Beta			Lower Bound	Upper Bound
1	(Constant)	48.162	1.704		28.267	.000	44.820	51.504
	AGE OF RESPONDENT	-.458	.035	-.325	-13.221	.000	-.526	-.390
a. Dependent Variable: NUMBER OF HOURS WORKED LAST WEEK

Charts (Figure 1.)