Chapter 8 Regression and Correlation 327The MS (mean square) column displays the sum of squares divided by
the degrees of freedom. Note that the mean square for the residual is equal
to the square of the standard error in cell B7^1 7.5447^25 56.9218^2. Thus you
can use the mean square for the residual to derive the standard error.
The next column displays the ratio of the mean square for the regression
to the mean square error of the residuals. This value is called the F ratio. A
large F ratio indicates that the regression may be statistically signifi cant. In
this example, the ratio is 45.7. The p value is displayed in the next column
and equals 0.0000092. Because the p value is less than 0.05, the regression
is statistically signifi cant. You’ll learn more about analysis of variance and
interpreting ANOVA tables in an upcoming chapter.Parameter Estimates and Statistics
The fi le output table created by the Analysis ToolPak Regression command
displays the estimates of the regression parameters along with statistics
measuring their signifi cance. See Figure 8-12.Figure 8-12
Parameter
estimates
and statistics
As you’ve already seen, the constant coeffi cient, or intercept, equals about
–21.79, and the slope based on the temperature variable is about 2.36. The
standard errors for these values are shown in the Standard Error column
and are 15.672 and 0.349, respectively. The ratio of the parameter estimates
to their standard errors follows a t distribution with n 22 , or 14, degrees
of freedom. The ratios for each parameter are shown in the t Stat column, and
the corresponding two-sided p values are shown in the P value column. In
this example, the p value for the intercept term is 0.186, and the p value
for the slope term (labeled Temperature) is 9.2 31026 , or 0.0000092 (note
that this is the same p value that appeared in the ANOVA table).
The fi nal part of this table displays the 95% confi dence interval for each
of the terms. In this case, the 95% confi dence interval for the intercept term
is about ( 2 55.41, 11.82), and the 95% confi dence interval for the slope is
(1.61, 3.11).
Note: In your output the confi dence intervals might appear twice. The fi rst
pair, a 95% interval, always appears. The second pair always appears, but
with the confi dence level you specify in the Regression dialog box. In this
case, you used the default 95% value, so that interval appears in both pairs.
What have you learned from the regression statistics? First of all,
you would decide to reject the null hypothesis and accept the alternative