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Coefficient of CorrelationLinear Regression, Scatter Diagram,
Coefficient of Determination, Pearson Product Moment Correlation Coefficient
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
3
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 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
3
4
5
6
f(x) = 0.717741935483871 x + 0.967741935483871R² = 0.939397533206831
Axis Title
Axis Title 939.02 r
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
Correlation AnalysisHow strong is the “relationship” between the
variables x and y?
Coefficient Analysis shows the strength of relationship between x and y.