CHAPTER 4: TWO VARIABLE ANALYSIS

E370 2013 Spring

Two-variable Analysis

Scatter plot

Covariance

Correlation coefficient

Least squares line

Scatter Plot

Collection of points: first step to analyze two variable relationships

Excel: Highlight two columns of data >> “Insert” menu>> “Scatter” button

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101214161820

Years of education and education of the mother

Years of education of the mother

Years

of

Educati

on

Covariance

Measure of the strength of a linear relationship between two variables (direction)

Positive covariance Positive linear relationship Negative covariance Negative linear relationship Zero covariance No linear relationship

Population Covariance

(=COVARIANCE.P(array 1, array 2))

Sample Covariance

(=COVARIANCE.S(array 1, array 2))

Relation

N

YXn

iYiXi

XY

1

))(( 1

))((1

N

YYXXs

n

iii

XY

1*

N

Ns

XYXY

Correlation coefficient

Unit-free measure of linear relationship (strength) Excel: =CORREL(array1, array 2) The higher the correlation coefficient in absolute value,

the stronger the relationship:

Population Correlation

Sample Correlation

YX

XYXY

YX

XY

ss

sr

11 XY

rXY

Least squares line

Unique line that describes the relationship between two variables, when one has been determined to cause the other.

Excel: “Add trendline” by right clicking the scatter plot. Check “display equation on Chart.”

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2

4

6

8

10

12

14

f(x) = − 0.0507917360167362 x + 8.28687937777992

.

Hours of SleepLinear (Hours of Sleep)

Hours of Work

Hours

of

Sle

ep