Page 17 - FINAL CFA II SLIDES JUNE 2019 DAY 3

LOS 8.h: Distinguish between and interpret the READING 8: MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS
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2
R and adjusted R in multiple regression.
MODULE 8.4: COEFFICIENT OF DETERMINATION & ADJUSTED R-SQUARED
COEFFICIENT OF DETERMINATION, R 2

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As we just demonstrated, the F & R tests can assess effectiveness of the entire set of independent variables in explaining the dependent
variable, e.g. the % of variation in the dependent variable that is collectively explained by all of the independent variables.

For a regression with one independent variable, the
correlation between the independent variable and
dependent variable is the same as multiple R (with
the same sign as the sign of the slope coefficient):

Multiple R is the square root of R .
2

Adjusted R 2

Unfortunately, R by itself may not be a reliable measure of the explanatory power of the multiple regression model. This is because R 2
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almost always increases as variables are added to the model, even if the marginal contribution of the new variables is not statistically
significant.

This problem is called overestimating the regression : a relatively high R may reflect the impact of a large set of
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independent variables rather than how well the set (‘’collective’’) explains the dependent variable.

To overcome this, we adjust R for
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the number of independent variables by: