Page 342 - The Handbook for Quality Management a Complete Guide to Operational Excellence

328 C o n t i n u o u s I m p r o v e m e n t A n a l y z e S t a g e 329

R Square. The square of multiple R, it measures the proportion of total
variation about the mean explained by the regression. For the example,
R = 0.717, which indicates that the fitted equation explains 71.7 percent
2
of the total variation about the average satisfaction level.
Adjusted R Square. A measure of R “adjusted for degrees of freedom,”
2
which is necessary when there is more than one independent variable.
Standard error. The standard deviation of the residuals. The residual is
the difference between the observed value of y and the predicted value
y’ based on the regression equation.
Observations. Refer to the number of cases in the regression analysis, or n.
ANOVA, or ANalysis Of Variance. A table examining the hypothesis that
the variation explained by the entire regression is zero. If this is so,
then the observed association could be explained by chance alone. The
rows and columns are those of a standard one-factor ANOVA table.
For this example, the important item is the column labeled “Significance
F.” The value shown, 0.00, indicates that the probability of getting
these results due to chance alone is less than 0.01; that is, the association
is probably not due to chance alone. Note that the ANOVA applies to
the entire model, not to the individual variables. In other words, the
ANOVA tests the hypothesis that the explanatory power of all of the
independent variables combined is zero.

The next table in the output examines each of the terms in the linear
model separately. The intercept is as described above; it corresponds to our
term a in the linear equation. Our model uses two independent variables.
In our termi nology, staff = b , food = b . Thus, reading from the coefficients
2
1
column, the linear model is:
Satisfaction = –1.188 + 0.902 * staff + 0.379 * food + error

The remaining columns test the hypotheses that each coefficient in the
model is actually zero.
Standard error column. Gives the standard deviations of each term, that
is, the standard deviation of the intercept = 0.565, etc.
t Stat column. The coefficient divided by the t statistic; that is, it shows
how many standard deviations the observed coefficient is from zero.

P-value. Shows the area in the tail of a t distribution beyond the
computed t value. For most experimental work a P value less that 0.05
is accepted as an indication that the coefficient is significantly different
from zero.
Lower 95% and upper 95% columns. A 95 percent confidence interval on
the coefficient. If the confidence interval does not include zero, we will
reject the hypothesis that the coefficient is zero.

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