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.
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.
Cell
Statistic / Parameter
Regression Statistics
B5
B6
B7
B8
R2 - coefficient of determination
R 2 - adjusted coefficient of determination
ˆ - standard error of the residuals
n, the number of observations
ANOVA
k – 1, degrees of freedom for the regression = number of parameters
estimated minus one
n – k degrees of freedom = number of observations minus the number of
parameters estimated
n – 1, degrees of freedom associated with the total sum of squares
SSR - sum of squared regression or explained
SSE - sum of squared residual or error
SST – sum of squared total
F-statistic for the null hypothesis 2 = 3 = . . . = k = 0. No linear
relationship between the x’s and y
p-value associated with the F-statistic
B12
B13
B14
C12
C13
C14
E12
F12
Estimated Parameters
A17 – A19
B17
B18
B19
C17-C19
D17-D19
E17-E19
F17-G19
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.
Estimated intercept
Estimated parameter associated with age
Estimated parameter associated with education
Estimated standard errors associated with each parameter
t-statistic associated with the null hypothesis j = 0. t-statistic is given by
the estimated coefficient divided by its standard error
p-values associated with the t-statistic
Upper and lower bounds associated with a 95% confidence interval.