Question

The manager of an amusement park would like to be able to predict daily attendance to develop more accurate plans about how much food to order and how many ride operators to hire. After some consideration, he decided that the following three factors are critical:

• Yesterday’s attendance
• Weekday or weekend (1 if weekend, 0 if a weekday)
• Predicted weather
  • Rain forecast ( 1 if the forecast for rain, 0 if not)
  • Sun   ( 1 if mostly sunny, 0 if not)

He then took a random sample of 40 days. For each day, he recorded the attendance, the previous day’s attendance, day of the week, and weather forecast. An example of the first few lines of Data and the regression output are below:

Regression Statistics
Multiple R	0.836766353
R Square	0.700177929
Adjusted R Square	0.665912549
Standard Error	810.7745532
Observations	40
ANOVA
	df	SS	MS	F	Significance F
Regression	4	53729535	13432384	20.43398	9.28E-09
Residual	35	23007438	657355.4
Total	39	76736973
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	3490.466604	469.1554	7.439894	1.04E-08	2538.031	4442.903
YestAtt	0.368547078	0.077895	4.731349	3.6E-05	0.210412	0.526682
I1	1623.095785	492.5497	3.295294	0.002258	623.1668	2623.025
I2	733.4646317	394.3718	1.85983	0.071331	-67.1527	1534.082
I3	765.5429068	484.6621	-1.57954	0.123209	-1749.46	218.3734

1. Test to see if the model is valid. Use alpha = .05 please give detailed answer values.
2. Can we conclude that weather is a factor in determining attendance? please give detailed answer values.

If the manager is looking for a way to help predict attendance, Is this a good model to use? How would you suggest making this model better? please give a detailed answer with values.

Answer 1

To get the validity of the model , the F test is used

Here the F statistic is significant which implies that our model fit the data well than the intercept only model .

To check whether weather is a factor in determining the attendance, t test is used

Here p value(.123)for weather is greater than .05, we conclude that the variable weather does not affect the attendance significantly.

This model has R² value(.7002) , which implies it is good model to use but removing the insignificant variables weather and type of day , we can get even a better model to predict the attendance well