RESEARCH METHODS HANDBOOK

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Contents	Introduction	Descriptive	Hypothesis	Tables	Appendix

Example: Simple Linear Regression

The following data were collected to estimate the correlation between years of formal education and income at age 35 and are the same data used in an earlier example to estimate Pearson r.

	Susan	Bill	Bob	Tracy	Joan
Education (years)	12	14	16	18	12
Income ($1000)	25	27	32	44	26

	Education	Income
	(Years)	($1000)
Name	X	Y	XY	X²	Y²
Susan	12	25	300	144	625
Bill	14	27	378	196	729
Bob	16	32	512	256	1024
Tracy	18	44	792	324	1936
Joan	12	26	312	144	676
=	72	154	2294	1064	4990
=	5
=	14.4	30.8

Determine Regression Line

Estimate the slope (b)

Estimate the y intercept

Given x (education) of 15 years, estimate predicted Y

or an estimated annual income of $32,485 for a person with 15 years of education

Determine the Standard Error of the Estimate

Standard error of the estimate of Y

Name	X	Y	a	b
Susan	12	25	-9.649	2.809	24.059	.941	.885
Bill	14	27	-9.649	2.809	29.677	-2.677	7.166
Bob	16	32	-9.649	2.809	35.295	-3.295	10.857
Tracy	18	44	-9.649	2.809	40.913	3.087	9.530
Joan	12	26	-9.649	2.809	24.059	1.941	3.767
=	5
=	14.4	30.8				=	32.205

Determine the Confidence interval for predicted Y

where

Degrees of Freedom (df) = 5-2 or 3

Alpha .05, 2-tailed

Based on the t-distribution (see table) t_cv= 3.182

Confidence interval for conditional Y

Given a 5% chance of error, the estimated income for a person with 15 years of education will be $32,485 plus or minus $10,424 or somewhere between $22,060 and $42,909.