Tutorial on Reading the Excel OLS Regression Output



Tutorial on Reading the Excel OLS Regression Output

The following figures provide information on how to read the output obtained from running an OLS regression in Excel. In this example, the dependent variable, income, is a function of two independent variables, age and number of years of education. Input data for this example is given in the following figure.

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See Tutorial 1 for information on the mechanics to run a regression in Excel. Using the above data, the OLS regression output from Excel is given in the following figure. Below the figure is an explanation of the output by cell that is relevant for this class. For further explanation of the statistics / parameters, see the class notes and reading assignments.

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Cell Statistic / Parameter

Regression Statistics

B5 R2 - coefficient of determination

B6 [pic]- adjusted coefficient of determination

B7 [pic]- standard error of the residuals

B8 n, the number of observations

ANOVA

B12 k – 1, degrees of freedom for the regression = number of parameters estimated minus one

B13 n – k degrees of freedom = number of observations minus the number of parameters estimated

B14 n – 1, degrees of freedom associated with the total sum of squares

C12 SSR - sum of squared regression or explained

C13 SSE - sum of squared residual or error

C14 SST – sum of squared total

E12 F-statistic for the null hypothesis (2 = (3 = . . . = (k = 0. No linear relationship between the x’s and y

F12 p-value associated with the F-statistic

Estimated Parameters

A17 – A19 Gives the names of variables each parameter is associated with. If you do not use labels, the names are X Variable 1, X Variable 2, etc.

B17 Estimated intercept

B18 Estimated parameter associated with age

B19 Estimated parameter associated with education

C17-C19 Estimated standard errors associated with each parameter

D17-D19 t-statistic associated with the null hypothesis (j = 0. t-statistic is given by the estimated coefficient divided by its standard error

E17-E19 p-values associated with the t-statistic

F17-G19 Upper and lower bounds associated with a 95% confidence interval.

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