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

01FEB2014
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

Userdefined 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. (2tailed)


.000


N

1495

1485


NUMBER OF HOURS WORKED LAST WEEK

Pearson Correlation

.325^{**}

1

Sig. (2tailed)

.000



N

1485

1490


**. Correlation is significant at the 0.01 level (2tailed).

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. (2tailed)


.000


N

1495

1485


NUMBER OF HOURS WORKED LAST WEEK

Pearson Correlation

.325^{**}

1

Sig. (2tailed)

.000



N

1485

1490


**. Correlation is significant at the 0.01 level (2tailed).

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. (1tailed)

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/Removed^{a}


Model

Variables Entered

Variables Removed

Method

1

AGE OF RESPONDENT^{b}

.

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

.325^{a}

.105

.105

22.302

a. Predictors: (Constant), AGE OF RESPONDENT

ANOVA^{a}


Model

Sum of
Squares

df

Mean
Square

F

Sig.


1

Regression

86941.814

1

86941.814

174.798

.000^{b}

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

Coefficients^{a}


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.)
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