Question

Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? r=-0.968

Answer 1

Given: Linear correlation coefficient = -0.968

Coefficient of determination, r², is an output measures of regression that explains how well the model fits the data, and how effectively can it predict the future outcomes.

It determines the amount of variation in the response (dependent) variable that is explained by the explanatory (independent) variable.

It is obtained by squaring the correlation coefficient r and hence ranges from 0 to 1.

A value close to one indicates a good fit and close to 0 implies that the explanatory variable contributes little towards explaining the response phenomenon.Here,

r² = (-0.968)² = 0.937.

The coefficient of determination implies that 93.7% of the variation of the data about the regression line is explained by the predictor.

The unexplained variation is obtained as:

1 - 0.937 = 0.063 = 6.3%

It implies that abot 6.3% of the total variation goes unexplained.

r² can also be obtained using the formula:

where, ESS = Explained sum of squares (Measure of explained variation in response variable)

TSS = Total sum of squares

SSR = Sum of squares due to residuals (Measure of unexplained variation in response variable)