Home |
Search |
Today's Posts |
#1
|
|||
|
|||
Regression Output -- R Square versus Adjusted R Square
The output from the regression function includes output values for both an "R
Square" and an "Adjusted R Square". Does anyone know what the difference is between these two values? The equations that are being used to produce them? -- Bonnie |
#2
|
|||
|
|||
Regression Output -- R Square versus Adjusted R Square
GOOGLE IT
ADJUSTED R_SQUARE R_Square (the Coefficient of Determination) is the percent of the Total Sum of Squares that is explained; i.e., Regression Sum of Squares (explained deviation) divided by Total Sum of Squares (total deviation). This calculation yields a percentage. It also has a weakness. The denominator is fixed (unchanging) and the numerator can ONLY increase. Therefore, each additional variable used in the equation will, at least, not decrease the numerator and will probably increase the numerator at least slightly, resulting in a higher R_Square, even when the new variable causes the equation to become less efficient(worse). In theory, using an infinite number of independent variables to explain the change in a dependent variable would result in an R_ Square of ONE. In other words, the R_Square value can be manipulated and should be suspect. The Adjusted R_Square value is an attempt to correct this short_coming by adjusting both the numerator and the denominator by their respective degrees of freedom. _ R2 = 1- (1 - R2 )((n - 1)/(n - k - 1)) whe R2 = Coefficient of Determination _ R2 = Adjusted Coefficient of Determination n = number of observations k = number of Independent Variables for example: when R2 =.9; n=100; and k=5; then _ R2 = 1 - (1 - .9)((100 - 1)/(100 - 5 - 1)) = 1 - (1 - .9)(99/94) = 1 - (.1)(1.05319) = 1 - .105319 = .89468 Unlike the R_Square, the Adjusted R_Square can decline in value if the contribution to the explained deviation by the additional variable is less than the impact on the degrees of freedom. This means that the Adjusted R_Square will react to alternative equations for the same dependent variable in a manner similar to the Standard Error of the Estimate; i.e., the equation with the smallest Standard Error of the Estimate will most likely also have the highest Adjusted R_Square. A final caution, however, is that while the R_Square is a percent, the Adjusted R_Square is NOT and should be referred to as an index value. "Bonnie" wrote: The output from the regression function includes output values for both an "R Square" and an "Adjusted R Square". Does anyone know what the difference is between these two values? The equations that are being used to produce them? -- Bonnie |
Reply |
Thread Tools | Search this Thread |
Display Modes | |
|
|
Similar Threads | ||||
Thread | Forum | |||
Recalculating a Regression Output in Data Analysis | Excel Worksheet Functions | |||
Mutiple Regression output | Excel Discussion (Misc queries) |