Correlation and Linear Regression

Tools:Scatterplot, correlation coefficient,

linear regression

If two variables are somehow related, there would be some trend in the scatter plot.

1. Scatterplot1. Scatterplot

Scatterplot Q2Scatterplot Q2

Linearity; Direction; Outlier

ScatterplotScatterplot

Measure the strenght of the linear relationship of two variables.

Sign: + , - Magnitude: [-1,1]

Partial correlation

2. Correlation Coefficient2. Correlation Coefficient

•Pearson correlation

Correlation Coefficient Q3Correlation Coefficient Q3

Partial Correlation Coefficent

Assumptions: Error follows a normal distribution with mean

0 and constant standard deviation σ.

Error Or,

)|(

10

10

XY

XXY

Regression ModelRegression Model

Regression Q1 e)Regression Q1 e)

Regression OutputRegression Output

ZY 212.907.

:line Regression^

Q1 e) iii. Independent two-sample t test Q1 e) iii. Independent two-sample t test vs. t-test about the slope in regression vs. t-test about the slope in regression modelmodel

0:H testing

toequivalent is :H testingSo,

(Smoker) 1 Z; )(Nonsmoker 0Z

10

SmokerNonsmoker0

10Smoker

0Nonsmoker

10

ZY

Regression cont. Q4Regression cont. Q4

Check normality? same constant standard deviation?

Data Transform data Recode into different variables

Data Select cases

Analyze Descriptive Explore (QQ Plot)

Analyze Compare Means Independent samples t-test (One sided!)