Hogs & Dawgs is an ice cream parlor on the border of north-central Louisiana and southern Arkansas that serves 43 flavors of ice creams, sherbets, frozen yogurts, and sorbets. During the summer Hogs & Dawgs is open from 1:00 p.m. to 10:00 p.m. on Monday through Saturday, and the owner believes that sales change systematically from hour to hour throughout the day. She also believes her sales increase as the outdoor temperature increases. Hourly sales and the outside temperature at the start of each hour for the last week are provided in the WEBfile IceCreamSales.
a. Construct a time series plot of hourly sales and a scatter plot of outdoor temperature and hourly sales. What types of relationships exist in the data?
b. Use a simple regression model with outside temperature as the causal variable to develop an equation to account for the relationship between outside temperature and hourly sales in the data. Based on this model, compute an estimate of hourly sales for today from 2:00 p.m. to 3:00 p.m. if the temperature at 2:00 p.m. is 93°.
c. Use a multiple linear regression model with the causal variable outside temperature and dummy variables as follows to develop an equation to account for both seasonal effects and the relationship between outside temperature and hourly sales in the data in the data: Hour1 = 1 if the sales were recorded between 1:00 p.m. and 2:00 p.m., 0 otherwise; Hour2 = 1 if the sales were recorded between 2:00 p.m. and 3:00 p.m., 0 otherwise; . . . Hour8 = 1 if the sales were recorded between 8:00 p.m. and 9:00 p.m., 0 otherwise. When the values of the 8 dummy variables are equal to 0, the observation corresponds to the 9:00-to-10:00-p.m. hour. Based on this model, compute an estimate of hourly sales for today from 2:00 p.m. to 3:00 p.m. if the temperature at 2:00 p.m. is 93°.
d. Is the model you developed in part b or the model you developed in part c more effective? Justify your answer.