MultivariateRegressionInExcel

2522154 05248141 10343474 03281995 06468430 00929805

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Unformatted text preview: 279707 -0.2522154 0.5248141 1.0343474 0.3281995 0.6468430 -0.0929805 -0.1832538 0.2017764 0.3976778 … … Percentile 0.2824859 0.8474576 1.4124294 1.9774011 2.5423729 3.1073446 3.6723164 4.2372881 4.8022599 5.3672316 … lsalary 4.605170 4.859812 5.159055 5.220356 5.384495 5.501258 5.505332 5.575949 5.598422 5.703783 … 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 ˆ 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 Regression Statistics Multiple R 0.5469128 R Square 0.2991136 Adjusted R Square 0.2910574 Standard Error 0.5102944 Observations 177 Sample estimate of the Percentage of variation in the dependent variable explained by the model Similar to R Square but penalizes extra independent variables 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.

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