STAT 1301STAT 1301

Chapter 8Chapter 8

Scatter Plots, CorrelationScatter Plots, Correlation

For Regression Unit For Regression Unit You Should KnowYou Should Know

How to plot pointsHow to plot points Equation of a lineEquation of a line

Y = mX + bY = mX + b m = slope m = slope b = Y-intercept b = Y-intercept

Plotting line from equationPlotting line from equationY = 3X + 2Y = 3X + 2

Data SetData Set

X YX Y

1 51 5

3 93 9

4 74 7

5 15 1

7 137 131 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

1212

1010

88

66

44

22

00

YY

XX

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

1212

1010

88

66

44

22

00

YY

XX

X YX Y

00 2 2

3 11 3 11

Y = 3X + 2Y = 3X + 2

..

..

For Regression Unit For Regression Unit You Should KnowYou Should Know

How to plot pointsHow to plot points Equation of a lineEquation of a line

Y = mX + bY = mX + b m = slope m = slope b = b = Y-interceptY-intercept

Plotting line from equationPlotting line from equationY = 3X + 2Y = 3X + 2

Chapter 7 - Good Review if neededChapter 7 - Good Review if needed

HistogramHistogram displays distribution of 1 variabledisplays distribution of 1 variable

Scatter DiagramScatter Diagram displays displays joint distribution joint distribution of 2 of 2

variables variables plots data as “points” in theplots data as “points” in the “x-y “x-y

plane.”plane.”

Association Between Two Association Between Two VariablesVariables

• indicates that knowing one helps in predicting the otherindicates that knowing one helps in predicting the other

Linear AssociationLinear Association• our interest in this courseour interest in this course• points “swarm” about a linepoints “swarm” about a line

Correlation AnalysisCorrelation Analysis• measures the strength of measures the strength of linearlinear association association

Hypothetical Father-Son DataHypothetical Father-Son Data

(association)(association)

Regression AnalysisRegression Analysis

we want to predict the we want to predict the dependentdependent variablevariable using the using the independent independent variablevariable

DependentDependentVariableVariable

(Y)(Y)

Independent Variable (X)Independent Variable (X)

Correlation CoefficientCorrelation Coefficient- measures linear - measures linear

associationassociation

-1 0 +1-1 0 +1

perfect no perfectperfect no perfect

negative linear positivenegative linear positiverelationship relationship relationshiprelationship relationship relationship

We use the letter “ r ” to denote the correlation We use the letter “ r ” to denote the correlation coefficient.coefficient.

Positive CorrelationPositive Correlation - - high values of one variable are associated with- - high values of one variable are associated with

high values of the other high values of the other

Examples:Examples: Father’s height, Father’s height,

son’s heightson’s height daily grade, final daily grade, final

gradegrade r = 0.93 for plot on r = 0.93 for plot on

the leftthe left 1 2 3 4 5 6 7 81 2 3 4 5 6 7 8

33

22

11

00

Negative CorrelationNegative Correlation - -- - high with low, low with highhigh with low, low with high

Examples:Examples: Car weight, Car weight,

miles per gallonmiles per gallon Days absent, final Days absent, final

gradegrade r = - 0.89 for plot r = - 0.89 for plot

shown hereshown here 1 2 3 4 5 6 71 2 3 4 5 6 7

44

33

22

11

00

Zero CorrelationZero Correlation - - no linear relationship- - no linear relationship

Examples:Examples: height, IQ scoreheight, IQ score r = 0.0 for plot r = 0.0 for plot

herehere

1 2 3 4 5 6 71 2 3 4 5 6 7

55

44

33

22

11

00

-.75, 0, .5, .99-.75, 0, .5, .99

r = 0.00r = 0.00

r = 0.40r = 0.40

r = - 0.60r = - 0.60

r = 0.8r = 0.8

r = 0.95r = 0.95