Two sets of regression equation are given for the full-model -- all independent variables added:

1. Partial Regression Equation - uses the raw data

2. Standardized Partial Regression Equation - uses data in z=score form

The Coefficient of Determination (Goodness of Fit) = 82.7% -- That is, 82.7% of the variation of Sepal Length is accounted for by variation of the three independent variables.

The Multiple Correlation Coefficient (R) = 0.909

All Possible Pairs

The correlation between each independent variable and the dependent variable is computed:

1. Petal L = 0.855 -- 73%
2. Petal W = 0.800 -- 64%
3. Sepal W = 0.114 -- 1.3%

The multiple correlations between each pair of independent variables and the dependent variable are:

2. Petal L & Sepal W = 0.899 -- 80.8%
3. Petal L & Petal W = 0.859 -- 73.7%
4. Sepal W & Sepal W = 0.823 -- 67.7%

Note that two variables -- Petal L and Sepal W account for 80.8% of the variation of Sepal L whereas all three variables accounted for 82.7%. The, addition of the third variable -- Petal W -- only increases the Coefficient of Determination by 1.9%.

Sometimes multiple regression analysis is used to be able to predict values of the dependent variable but sometimes it is more important to look at the sequence in which the independent variables are added to the predicting equation.

Return to the Multiple Regression Analysis