Question

Using High School Longitudinal Study dataset, construct a research question that can be answered with a Pearson correlation and bivariate regression.
Do not forget to evaluate if the correlation and bivariate regression assumptions are met and report the effect size. In your analysis, display the data for the output.

Answer 1

I want to test if there is any significant relationship between age and Lived Poverty Index (average index of 5 poverty items). My dependent variable is Lived Poverty Index. My independent variable is age. Both these variables are measured on ratio scale of measurement. ratio scales have equal differences between scale values have equal quantitative meaning. Ratio scales have a true zero point. A true zero point means that a value of zero on the scale represents zero quantity of the construct being assessed.

The SPSS output for Pearson correlation between age and Lived Poverty Index is given below. With r=0.044 and p-value < 0.05 (alpha), I conclude that value of correlation coefficient is significant. with r = 0.044 I can say that there is an extremely weak positive linear relationship or almost no linear relationship between age and Lived Poverty Index. That is as the value of age increases there is no effect on Lived Poverty Index.

Correlations
		Lived Poverty Index (average index of 5 poverty items)	Q1. Age
Lived Poverty Index (average index of 5 poverty items)	Pearson Correlation	1	.044**
	Sig. (2-tailed)		.000
	N	50923	50488
Q1. Age	Pearson Correlation	.044**	1
	Sig. (2-tailed)	.000
	N	50488	51143
**. Correlation is significant at the 0.01 level (2-tailed).

The linear regression analysis output as obtained from SPSS is given below.

Variables Entered/Removeda
Model	Variables Entered	Variables Removed	Method
1	Q1. Ageb	.	Enter
a. Dependent Variable: Lived Poverty Index (average index of 5 poverty items)
b. All requested variables entered.

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.044a	.002	.002	.9436
a. Predictors: (Constant), Q1. Age

ANOVAa
Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	87.324	1	87.324	98.067	.000b
	Residual	44955.409	50486	.890
	Total	45042.733	50487
a. Dependent Variable: Lived Poverty Index (average index of 5 poverty items)
b. Predictors: (Constant), Q1. Age

With F = 98.067 and p-value < 0.05, I can say that model is significant. Coefficient of determination R^2 = 0.002. This implies only .2% variation in the dependent variable is explained by the independent variable. Hence model is not a good fit to the data.