RegressionMBA/510 Week 5

Objectives

• Describe the use of correlation in making business decisions

• Apply linear regression and correlation analysis.

• Interpret the output produced by a multiple regression analysis.

Correlation in Business Decision-Making

Correlation Analysis

The Independent Independent VariableVariable provides the basis for estimation. It is the predictor variable.

Correlation AnalysisCorrelation Analysis is a group of statistical techniques to measure the association between two variables.

A Scatter DiagramScatter Diagram is a chart that portrays the relationship between two variables.

The Dependent Dependent VariableVariable is the variable being predicted or estimated.

Advertising Minutes and $ Sales

0

5

10

15

20

25

30

70 90 110 130 150 170 190

Advertising Minutes

Sale

s ($

thou

sand

s)

Negative values indicate an inverse relationship and positive values indicate a direct relationship.

The Coefficient of CorrelationCoefficient of Correlation (r) is a measure of the strength of the relationship between two variables.

-1 10

P earson's r

Also called Pearson’s r and Pearson’s product moment correlation coefficient.

It requires interval or ratio-scaled data.

It can range from -1.00 to 1.00.

Values of -1.00 or 1.00 indicate perfect and strong correlation.

Values close to 0.0 indicate weak correlation.

0 1 2 3 4 5 6 7 8 9 10

10 9 8 7 6 5 4 3 2 1 0

X

Y

Perfect Negative Correlation

0 1 2 3 4 5 6 7 8 9 10

10 9 8 7 6 5 4 3 2 1 0

X

Y

Perfect Positive Correlation

0 1 2 3 4 5 6 7 8 9 10

10 9 8 7 6 5 4 3 2 1 0

X

Y

Zero Correlation

0 1 2 3 4 5 6 7 8 9 10

10 9 8 7 6 5 4 3 2 1 0

X

Y

Strong Positive Correlation

Correlation “test”

• Is this a positive or negative correlation?

• Why might we find a relationship?

The longer couples have been together the more similar they are

in their attitudes and opinions.

A researcher finds that students who attend fewer classes get poorer grades.

Cities with more stores selling pornography have higher

rates of violence.

In each case above there was more than one explanation for why we might find the relationship between the variables.  Since we cannot rule out these alternative explanations, we cannot conclude that changes in one variable "caused" changes in the other variable. Thus, CORRELATION does not equal CAUSATION.

Group Exercise 1

Group Exercise 1 cont

y = 1.1842x + 18.947

R2 = 0.5761

20

30

40

50

60

70

80

0 10 20 30 40 50

Sales Calls (X)

Cop

iers

Sol

d (Y

)

Group Exercise 1 cont

• Situation 1: Goal next month 600

• Situation 2: New model came out last month

• Situation 3: Goal next month 900 because new model is coming out

Group Exercise 2

Group Exercise 2 cont

y = 1.9917x + 58.697

R2 = 0.703

74

76

78

80

82

84

86

88

5 7 9 11 13 15

Power Used

Tem

p (F

)

y = 1.7842x + 91.124

R2 = 0.1305

100

105

110

115

120

125

130

5 7 9 11 13 15

Power Used

Uni

ts P

rodu

ced

Group Exercise 2 cont

• Situation 1: Produced 125 units

• Situation 2: 90°F: How many units?

• Situation 3: How to control power used?