Question

Great Wolf Lodge Resorts tries to forecast monthly attendance. The management has noticed a direct relationship between the average monthly temperature and attendance.
Month   Average Temperature   Resort Attendance (in thousands)
1    24 43
2    41 31
3    32    39
4 30    38
5 38 35

Given five months of average monthly temperatures and corresponding monthly attendance, compute a linear regression equation of the relationship between the two. (Use Excel Data Analysis- Regression to derive forecasting equation and copy paste the output of the Data Analysis)

If next month’s average temperature is forecast to be 46 degrees, use your linear regression equation to develop a forecast.
Compute a correlation coefficient (r) for the data and determine the strength of the linear relationship between average temperature and attendance. How good a predictor is temperature for attendance? (Use Excel Data Analysis- Regression output to determine r, copy your output from Excel and paste it here.)

Answer 1

Regression output

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.97016126
R Square	0.941212871
Adjusted R Square	0.921617162
Standard Error	1.258305739
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	76.05	76.05	48.03158	0.006159581
Residual	3	4.75	1.583333
Total	4	80.8
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	58.65	3.145764348	18.64412	0.000337	48.63877387	68.66122613	48.63877387	68.66122613
X Variable 1	-0.65	0.093788572	-6.93048	0.00616	-0.948477095	-0.351522905	-0.948477095	-0.351522905

Regression equation this obtained: Resort attendance(in thousands) = 58.65-0.65*average temperature

So, if average temperature is 46, Resort attendance(in thousands) = 58.65-0.65*46 = 28.75

Correlation coefficient value = 0.97016126

Value of 0.97016126 is close to +1 which indicates temperature is a strong predictor of attendance and a strong positive linear relationship exists between attendance and temperature