Question

The manager of an amusement park would like to be able to predict daily attendance in order 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 weekday)
Predicted weather
Rain forecast ( 1 if 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:
Attendance   Yest Att   I1   I2   I3
7882   8876   0   1   0
6115   7203   0   0   0
5351   4370   0   0   0
8546   7192   1   1   0

SUMMARY OUTPUT                  
                      
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
Yest Att   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
Test to see if the model is valid. Use alpha = .05
Can we conclude that weather is a factor in determining attendance?
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 proper details for the answer. Thank you

Answer 1

Significance of Independent variable weather

From, the result summary,

	Coefficients	t Stat	P-value
Weather (I2)	733.4646317	1.85983	0.071331	>	0.05	Not Significant

The P-value for independent variable, weather is 0.071331 which is greater than 0.05 at 5% significance level hence we can conclude that weather is not a significant variable in the model.

Overall Significance

	F	Significance F
Regression	20.43398	9.28E-09	<	0.05	Significant

The significance F value is 9.28E-09 which is less than 0.05 at 5% significance level which mean the model significantly fit the data value at the predefined significance level (0.05). Hence we can conclude that independent variables fit the model significantly.

However, the regression model can be further improve by removing the insignificant independent variables.

From, the result summary,

	P-value
Yest Att	3.60E-05	<	0.05	Significant
I1	0.002258	<	0.05	Significant
I2	0.071331	>	0.05	Not Significant
I3	0.123209	>	0.05	Not Significant

There is only two variables, Yesterday Attendance and Weekday or weekend are statistically significant at 5% significance level. Hence by removing other two variable we can improve the model in terms of R-square value (The R-square value tell, how well the regression model fit the data values)