Interpreting the Regression Output from Excel
To use the regression facility in Excel, first be sure you have your data entered in columns. Click on
Tools, then on Data Analysis. From the list of options, choose Regression. A dialog box will open which
allows you to mark or otherwise designate the range for the x variable and the range for the y variable. You
should also mark the data label at the top of each column and place a check mark in the “Labels” box in the
dialog box. If you do not designate an area on the open worksheet to place the output, Excel will by default
create a new worksheet to receive the output. Generally speaking, it’s best to click on the radio button for
output range and choose a space next to your data to receive the output. Your output will look like this:
SUMMARY
OUTPUT
In simple regression, this number is the absolute
value of Pearson’s coefficient of correlation. Its
sign will be the same as that of the b1 coefficient.
Regression Statistics
Multiple R
0.795941592
R Square
0.633523017
Adjusted R Square
0.560227621
Standard Error
53.06706929
Observations
7
ANOVA
This number is the coefficient of determination
r2. It expresses the proportion of the variation in
y which is explained by variation in x.
ANOVA is not important in simple regression since it duplicates other tests.
1
5
6
SS
24340.85936
14080.56921
38421.42857
MS
24340.859
2816.1138
F
8.6434217
Significance
F
0.032257789
Coefficients
127.8233737
80.27609682
Standard Error
37.42460754
27.30507654
t Stat
3.41549
2.9399697
P-value
0.0189304
0.0322578
Lower 95%
31.62035737
10.08616307
df
Regression
Residual
Total
Intercept
Distance
This is the
label attached
to the x
variable.
This is the
slope of the
regression
line or b1.
Continued next page
This is the
standard
error of the
coefficient
which we’ve
called sb1
the t
statistic is
b1  sb1. It
has n-2
degrees of
freedom
Upper 95%
224.02639
150.4660306
This is the p-value of the
hypothesis test H0: β1 = 0. To
reject it is to conclude that there is
a significant relationship between x
and y. Note that it is also the pvalue of the test for the correlation
coefficient H0:  = 0.
SUMMARY
OUTPUT
Regression Statistics
Multiple R
0.795941592
R Square
0.633523017
Adjusted R Square
0.560227621
Standard Error
53.06706929
Observations
7
This is the standard error of the estimate,
which we’ve designated sy.x.
The number of observations or n.
ANOVA
1
5
6
SS
24340.85936
14080.56921
38421.42857
MS
24340.859
2816.1138
F
8.6434217
Significance
F
0.032257789
Coefficients
127.8233737
80.27609682
Standard Error
37.42460754
27.30507654
t Stat
3.41549
2.9399697
P-value
0.0189304
0.0322578
Lower 95%
31.62035737
10.08616307
df
Regression
Residual
Total
Intercept
Distance
We’ve struck through the line of
information for Intercept to emphasize that
these numbers are rarely of interest in
themselves. Although the intercept is used
as b0 in the regression equation and in
making predictions, we do not usually test
H0: β0 = 0.
These numbers are the limits of a confidence
interval for the slope of the regression line: we
are 95% confidenct that 10.09  β1  150.47.
Upper 95%
224.02639
150.4660306