Although the Excel regression output, shown in Figure 12.21 for Demonstration Problem 12.1, is somewhat different from the Minitab output, the same essential regression features are present. The...

Although the Excel regression output, shown in
Figure 12.21
for Demonstration Problem 12.1, is somewhat different from the Minitab output, the same essential regression features are present. The regression equation is found under Coefficients at the bottom of ANOVA. The slope or coefficient of
x
is 2.2315 and the
y-intercept is 30.9125. The standard error of the estimate for the hospital problem is given as the fourth statistic under Regression Statistics at the top of the output, Standard Error = 15.6491. The
r
²
value is given as 0.886 on the second line. The
t
test for the slope is found under
t
Stat near the bottom of the ANOVA section on the “Number of Beds” (x
variable) row,
t
= 8.83. Adjacent to the
t
Stat is the
p-value, which is the probability of the
t
statistic occurring by chance if the null hypothesis is true. For this slope, the probability shown is 0.000005. The ANOVA table is in the middle of the output with the
F
value having the same probability as the
t
statistic, 0.000005, and equaling
t
². The predicted values and the residuals are shown in the Residual Output section.

In addition to developing the regression model, plotting and commenting on the residuals, I'd like you to comment on the how well you regard the model from the standpoint of statistical significance as well as variance explained.

Extracted text: SUMMARY OUTPUT Regression Statistics Multiple R RSquare Adjusted R Square 0.942 0.886 0.875 Standard Error 15.6491 Observations 12 ANOVA df MS F. Significance F Regression Residual 1 19115.06322 19115.06 78.05 0.000005 10 2448.94 244.89 Total 11 21564 Coefficients Standard Error t Stat P-value 0.041888 Intercept Number of Beds 30.9125 13.2542 2.33 2.2315 0.2526 8.83 0.000005 RESIDUAL OUTPUT Observation Predicted FTES Residuals 1 82.237 -13.237 2 95.626 -0.626 95.626 6.374 4 109.015 8.985 124.636 1.364 6. 133.562 -8.562 7 142.488 -4.488 151.414 26.586 9. 173.729 -17.729 10 178.192 5.808 11 200.507 -24.507 12 204.970 20.030