Question

1. David is a street vendor who sells hot dogs in the city and would like to develop a regression model to help him predict the daily demand for his product in order to improve inventory control. David believes that the three main factors affecting hot dog demand for a particular day are his price per hot dog, the high temperature during business hours that day, and whether the day falls on a weekday or weekend (many of David’s customers are business people). To develop his model, David recorded data during 24 randomly selected days. The data can be found in the file “Hot- DogDemand1.csv” in the d2l. As demonstrated in the lecture, please create a subset data of size 16 and perform your statistical analysis for the subset data. Please note that the subset data should be a random sample of the given data.

(a) Write down the estimated multiple linear regression equations for weekday and weekend sepa- rately.

(b) Use your estimated regression equation to predict the daily demand for hotdogs at a $1.25 price on an 82?F weekend.

(c) Compute a 90% confidence interval for the coefficient of price using JMP. Interpret it in the context of the problem. Data:

Demand Temp. Price Day

144 73 1 Weekday

90 64 1 Weekend

108 73 1 Weekday
110 76 1 Weekday
112 78 1 Weekend
120 82 1 Weekday
126 86 1.2 Weekday
99 70 1.2 Weekend
54 45 1.2 Weekend
48 73 1.5 Weekend
90 75 1.5 Weekday
81 61 1.5 Weekday
49 72 1.5 Weekend
34 65 1.5 Weekend
92 77 1.5 Weekday
82 60 1.5 Weekday

Answer 1

-------------------------------------------------------------------------------------------------------------------------------------------

---------------------------------------------------------------------------------------------------------------------------------------

Interpretation:

We can be 90% confident that the estimated value of the demand with respect to price is between -107.5131 and -52.51142, keepling constant the other independent variables temperature and day.