## From Simple to Multiple Regressions

The regression that measures the relationship between two variables becomes a multiple regression when it is extended to include more than one independent variables (X1,X2,X3,X4..) in trying to explain the dependent variable Y. While the graphical presentation becomes more difficult, the multiple regression yields output that is an extension of the simple regression.

Y = a + b X1 + c X2 + dX3 + eX4 The R-squared still measures the strength of the relationship, but an additional R-squared statistic called the adjusted R squared is computed to counter the bias that will induce the R-squared to keep increasing as more independent variables are added to the regression. If there are k independent variables in the regression, the adjusted R squared is computed as follows -

1 The actual values that t statistics need to take on can be found in a table for the t distribution, which is reproduced at the end of this book as an appendix.

R squared =

Adjusted R squared =

Multiple regressions are powerful weapons that allow us to examine the determinants of any variable.

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