Question 2

The Fun and Crazy theme park is losing money during the off-season. Some days there are many customers and other days there are few. Every day they have 40 staff members working, but on some days, they have more staff working than they need, and on other days they don't have enough to service customers. They need a way to forecast demand so they can plan their resourcing better. The accountant suspects that ticket sale volumes might be related to the daily forecast maximum temperature - large volumes on hot days, and low volumes on cold days.

To test their theory, they randomly sample 20 off-season days from their records. For each of these days, they record the ticket sale volume (S) and they look through historical data to find the forecast of the maximum temperature in Celsius (T) for that day and the data is stored in the attached Excel file - TemperatureSales.xls.

a. Using the Excel data, construct a scatter plot. What do you conclude?

b. To analyse the relationship between Temperature and Sales, please utiliseExcel's Data Analysis add-in to conduct an OLS regression.You are required to copy the generated regression output from Excel and paste them into your answer document. Additionally, you are also required to upload the Excel file containing the regression output for reference.

c. From the Excel regression results obtained in part (b), find the equation to the line of best fit and interpret the slope coefficient. What conclusion do you make based on this?

d. At the 5% level of significant, is there evidence of a linear relationship between the temperature and ticket sales?

e. Construct a 95% confidence interval estimate of the slope. What can you conclude from this estimate?

f. Predict the daily mean ticket sales, when the temperature hits 30 degrees Celsius. Is this prediction reliable? Explain your answer.

g. Explain why it would not be appropriate to use the model to predict the ticket sales when the temperature hits 40degrees Celsius.

Sales: S (Y)	Temperature: T (X)
3366	28
4527	25
5207	31
1296	17
4045	19
2483	21
4394	28
2486	21
2637	18
5346	27
1518	17
650	16
3560	22
5386	28
7246	35
6172	28
5513	32
7720	34
3092	23
3113	22