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 15 and perform your statistical analysis for the subset data. Please note that the subset data should be a random sample of the given data.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 15 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 $1.20 price on an 80F temperature on a weekday.

(c) Compute a 94% confidence interval for the coefficient of temperature using JMP. Interpret it in the context of the problem.

Demand	Temperature	Price	Day
144	73	1	Weekday
90	64	1	Weekend
108	73	1	Weekday
110	76	1	Weekday
112	78	1	Weekend
114	77	1	Weekday
116	79	1	Weekday
120	82	1	Weekday
54	45	1.2	Weekend
69	54	1.2	Weekday
126	86	1.2	Weekday
99	70	1.2	Weekend
54	45	1.2	Weekend
69	54	1.2	Weekday
126	86	1.2	Weekday
99	70	1.2	Weekend
48	73	1.5	Weekend
33	66	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

Answer 2

To create a subset data of size 15 from the given data, you would randomly select 15 observations from the dataset. Make sure to use a random sampling method to ensure that the subset represents a random sample of the data.

Once you have your subset data, you can proceed with the statistical analysis. Let's address each question step by step:

(a) To estimate the multiple linear regression equations separately for weekdays and weekends, you would use the subset data and perform separate regression analyses for each category.

The regression equation for weekdays can be represented as:

Demand = β₀ + β₁ * Temperature + β₂ * Price

And the regression equation for weekends can be represented as:

Demand = γ₀ + γ₁ * Temperature + γ₂ * Price

In these equations, β₀ and γ₀ represent the intercepts, β₁ and γ₁ represent the coefficients for temperature, and β₂ and γ₂ represent the coefficients for price.

(b) To predict the daily demand for hotdogs at a $1.20 price on an 80°F temperature on a weekday, you would substitute the values into the weekday regression equation:

Demand = β₀ + β₁ * Temperature + β₂ * Price

Substituting the values: Price = 1.20 Temperature = 80

You can use the estimated coefficients from the regression analysis to calculate the predicted demand.

(c) Unfortunately, without access to JMP or the specific dataset, I am unable to perform the statistical analysis and compute the confidence interval for the coefficient of temperature. However, in general, a confidence interval provides a range of values within which we can be confident that the true population parameter lies. In this case, the confidence interval for the coefficient of temperature would indicate the range of values within which we can be 94% confident that the true effect of temperature on demand falls.

Interpreting the confidence interval would involve considering its lower and upper bounds. If the confidence interval for the coefficient of temperature includes zero, it would suggest that temperature may not have a statistically significant effect on demand. If the interval does not include zero, it would suggest that there is evidence of a significant relationship between temperature and demand.

I recommend using statistical software like JMP or other statistical packages to perform the regression analysis and compute the confidence interval based on your subset dat