Chapter 10 Analysis of Variance 409The analysis of variance table produced by the regression (cells A10:F14)
and shown in Figure 10-12 should appear familiar to you because it is equiv-
alent to the ANOVA table created earlier and shown in Figure 10-7. There are
two differences: the Between Groups row from the earlier ANOVA table is
the Regression row in this table, and the Within Groups row is now termed
the Residual row.
The parameter values of the regression are also familiar. The intercept co-
effi cient 481.125 (cell B17) is the same as the mean price in New York. The
values of the CHI, DEN, and SF effect terms now represent the difference be-
tween the mean hotel price in these cities and the price in New York. Note
that this is exactly what you calculated in the matrix of paired mean differ-
ences shown in Figure 10-9. The p values for these coeffi cients are the un-
corrected p values for comparing the paired mean differences between these
cities and New York. If you multiplied these p values by 6 (the number of
paired comparisons in the paired mean differences matrix), you would have
the same p values shown in Figure 10-9.
Can you see how the use of indicator variables allowed you to create the
effects model? Consider the values for I (“CHI”). For any non-Chicago hotel,
the value of the indicator variable is 0, so the effect term is multiplied by 0,
and therefore has no impact on the estimate of the hotel price. It is only for
Chicago hotels that the effect term is present.
As you can see, using regression analysis to fi t the effects model gives you
much of the same information as the one-way analysis of variance.
The model you’ve considered suggests that the average price for a single
room at a hotel in New York City is signifi cantly higher than that for a sin-
gle room in a hotel in Chicago, Denver, or San Francisco. You can expect
to pay about an average of $481 for a single room in New York City, and
$253.50 less than this in Chicago, $300 less in Denver, and $280.75 less
in San Francisco. You’ve completed your study of the hotel data in this
workbook. You can close the Hotel ANOVA workbook now, saving your
changes.
EXCEL TIPS
You can use the Regression command to calculate the means
model instead of the effects model. To do this, run the Analysis
ToolPak’s Regression command, choose all of the indicator
variables in the Input X Range text box, and select the Constant
Is Zero checkbox. This will remove the constant term from the
model. The parameter estimates will correspond to mean values
of the different groups.