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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 yoghurts, 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 DATAfile IceCreamSales.

Click on the datafile logo to reference the data.


Problem 8-27

 

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 yoghurts, 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 DATAfile IceCreamSales.

 

Click on the datafile logo to reference 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.

 

If required, round your answers to three decimal places. For subtractive or negative numbers use a

 

minus sign even if there is a + sign before the blank. (Example: -300)

 

Sales =

 

+

 

Temperature

 

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 93oF.

 

If required, round your answers to two decimal places.

 

$ (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.

 

Note that when the values of the 8 dummy variables are equal to 0, the observation corresponds

 

to the 9:00 P.M. to 10:00 P.M. hour.

 

If required, round your answers to three decimal places. For subtractive or negative numbers use a

 

minus sign even if there is a + sign before the blank. (Example: -300)

 

Sales =

 

+

 

Temperature +

 

Hour1 +

 

Hour2

 

+ Hour3 + Hour7 + Hour4 + Hour5 + Hour6 + Hour8 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 93oF.

 

If required, round your answers to two decimal places.

 

$

 

Is the model you developed in part (b) or the model you developed in part (c) more effective?

 

If required, round your answers to three decimal places.

 

Model developed in part

 

(b) Model developed in part (c) MSE Model developed in part (b)

 







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