Coefficient of CorrelationLinear Regression, Scatter Diagram,

Coefficient of Determination, Pearson Product Moment Correlation Coefficient

Linear Regression

Linear Regression

Why is it called LEAST SQUARES METHOD?

Linear Regression

Excel Demonstration to find regression equation

Coefficient of DeterminationHow good is the “FIT” between the actual data

and the regression equation?

The Coefficient of Determination shows a numerical measure about how good is the “fit” between actual observations (x,y) and the points generated by the regression equation

baxy ˆ

Coefficient of Determination

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

1

2

3

4

5

6

7

f(x) = 0.5 x + 1.3R² = 0.109649122807018

Axis Title

Axis Title

0 1 2 3 4 5 6 70

1

2

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4

5

6

f(x) = 0.717741935483871 x + 0.967741935483871R² = 0.939397533206831

Axis Title

Axis Title

0 1 2 3 4 5 6 70

1

2

3

4

5

6

f(x) = 0.717741935483871 x + 0.967741935483871R² = 0.939397533206831

Axis Title

Axis Title

Coefficient of DeterminationThe symbol for the coefficient of determination

is

1,0)range( 22 rr

Coefficient of Determination

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

1

2

3

4

5

6

7

f(x) = 0.5 x + 1.3R² = 0.109649122807018

Axis Title

Axis Title 109.02 r

0 1 2 3 4 5 6 70

1

2

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5

6

f(x) = 0.717741935483871 x + 0.967741935483871R² = 0.939397533206831

Axis Title

Axis Title 939.02 r

Coefficient of Determination

Coefficient of Determination

0 1 2 3 4 5 6 70

1

2

3

4

5

6

f(x) = 0.717741935483871 x + 0.967741935483871R² = 0.939397533206831

Axis Title

Axis Title

Coefficient of Determination

0 1 2 3 4 5 6 70

1

2

3

4

5

6

f(x) = 0.717741935483871 x + 0.967741935483871R² = 0.939397533206831

Axis Title

Axis Title

Coefficient of Determination

0 1 2 3 4 5 6 70

1

2

3

4

5

6

f(x) = 0.717741935483871 x + 0.967741935483871R² = 0.939397533206831

Axis Title

Axis Title

Coefficient of Determination

Correlation AnalysisHow strong is the “relationship” between the

variables x and y?

Coefficient Analysis shows the strength of relationship between x and y.

Coefficient Analysis

Correlation Coefficient

Correlation Coefficient Interpretation

10 r

Correlation Coefficient Interpretation

01 r

Correlation Coefficient Interpretation

0r

Correlation Coefficient

Correlation Coefficient

Correlation Coefficient

Correlation Coefficient

Final RemarksThe correlation coefficient r does not

necessarily indicate causation.

It does not demonstrate a cause-and-effect connection between variables.

It is a measure that demonstrates how frequently two variables x and y are observed to occur together.