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… 2 1. The Regression Coefficients Table We start with the regression coefficients table as this is the simplest to understand. It
contains statistics related to the estimates of the intercept and independent variable
coefficients in the linear regression model. ˆˆ
Column “Coefficient” shows the estimated regression coefficients b0 , b1 and b2 . Column
“Standard Error” shows the estimated standard deviations of the regression coefficient
estimates. Column “t Stat” shows the t-statistics of the estimated regression coefficients
computed by dividing the coefficient estimates by their standard errors. The t-statistic
of a regression coefficient indicates how significantly different from zero the coefficient is.
Column “P-value” gives the two-sided p-values of the corresponding t-statistics
according to a t distribution of n - p - 1 (in our example 177 - 2 - 1 = 174 ) degrees of freedom (This concept is explained in section “The ANOVA Table”). The p-value of a
test statistic is the probability of obtaining a more extreme observation (i.e. observation
in the tails) from a certain distribution.
Columns “Lower 95%” and “Upper 95%” define a 95% confidence interval for each
regression coefficient. 2. The Regression Statistics Table The following figure provides the interpretation of items in the regression statistics table:
Square root of R Square
Adjusted R Square
177 Sample estimate of the Percentage of variation in the dependent
variable explained by the model
Similar to R Square but penalizes extra
Number of observations used in the regression standard deviation of the
regression model error term VER. 2/2/2012. © P. KOLM 3 In the table above:
Multiple R is the correlation between the observed values of the dependent variable log(salary ) and its predicted values from the regression equation.
R Square is the squared value of multiple R, and can be viewed as a measure of the
overall goodness of fit of the regression model.
Since R Square will always increase as more independent variables are added to the
regression model, one often uses the Adjusted R Square which will only increase when
the additional independent variable increases the model’s explanatory power by more
than would be expected by chance.
The Adjusted R Square is computed as
R 2 = 1 - (1 - R 2 ) ⋅ (n - 1) / (n - p - 1), where...
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This document was uploaded on 02/17/2014 for the course COURANT G63.2751.0 at NYU.
- Fall '14