SCENARIO 1611 The manager of a health club has recorded mean

SCENARIO 16-11

The manager of a health club has recorded mean 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 - 2^nd Order Model

Regression Statistics
Multiple R 0.993
R Square 0.987
Adjusted R Square 0.985
Standard Error 9.276
Observations 15

Coefficients
Intercept 5.86
X Variable 1 0.37
X Variable 2 0.85

SUMMARY OUTPUT - 1^st Order Model

Regression Statistics
Multiple R 0.993
R Square 0.987

Adjusted R Square 0.985
Standard Error 9.150
Observations 15

Coefficients
Intercept 5.66
X Variable 1 1.10


Referring to Scenario 16-11, using the first-order model, the forecast of mean attendance for month 16 is ________.

Solution

Regression line for the first order model from the given output is

5.66+1.10 X where x is the value of 15th month

The forecast of mean attendance for month 16 is = 5.66+(1.1*263.5) = 295.51