Instruction 14-8
the Manager of a Health Club Has Recorded

Instruction 14-8
The manager of a health club has recorded average attendance in newly introduced step classes over the last 15 months: 32.1,39.5,40.3,46.0,65.2,73.1,83.7,106.8,118.0,133.1,163.3,182.8,205.6,249.1,and 263.5.She then used Microsoft Excel to obtain the following partial output for both a first- and second-order autoregressive model.
SUMMARY OUTPUT - 2nd Order Model
Regression Statistics
$\begin{array} { l r } \text { Multiple R } & 0.993 \\ \text { R Square } & 0.987 \\ \text { Adjusted R Square } & 0.985 \\ \text { Standard Error } & 9.276 \\ \text { Observations } & 15 \end{array}$
$\begin{array} { l c r } & \text { Coefficients } \\ & 5.86 & \\ \text { Intercept } & 0.37 & \\ \text { X Variable 1 } & 0.85 & \\ \text { X Variable 2 } & \\ & \\ \text { SUMMARY OUTPUT - 1st Order Model } \\ \text { Regression Statistics } & \\ \text { Multiple R } & 0.993 \\ \text { R Square } & 0.987 \\ \text { Adjusted R Square } & 0.985 \\ \text { Standard Error } & 9.150 \\ \text { Observations } & 15 \end{array}$
Coefficients
Intercept $\quad 5.66$
$X$ Variable $1 \quad 1.10$
-Referring to Instruction 14-8,based on the parsimony principle,the second-order model is the better model for making forecasts.