Project 1: Chapter 4 Draft 10 points and Final 20 points
This project must be typed and you may work in groups for this project (a maximum of three people). Answer the questions with complete sentences and use all the appropriate terms given in the notes or in the book. Include any graphs and state what software, calculator, or any other website you are using to do your calculation and graphs. The link for the data is in StatCrunch, but you can export it to an Excel file if you want. To do this, once you open the link, click on Data, Export, and then click on Export again to download the Excel file. A draft of the project will be due on Monday 05/16/22 by 11:59 pm and the complete project is due on Tuesday 05/17/21 by 11:59 pm. For the draft, at least, you must show that you are able to do the scatter plot and compute the linear regression line.
A national restaurant chain is composed of 6500 restaurants, each of which is located in close proximity to an interstate highway. The restaurant’s business strategy is to serve its core customer base: people traveling on the interstate highway system who are looking for a quality dining experience. Customers generally enjoy the restaurant chain’s menu, atmosphere, and consistency from restaurant to restaurant. The company’s leadership, located at corporate headquarters, is very interested in the relationship between the cost of a gallon of gasoline and the company’s revenue. Specifically, the company is concerned that if gasoline prices rise in the near future, the company’s revenue will decline dramatically. The company’s research department recently collected data for analysis in order to support leadership’s upcoming discussion of whether the company should expand and diversify to locations away from an interstate highway. Annual revenue figures from a random sample of 150 restaurants were collected. The research division also collected and calculated the average annual cost of gasoline at these 150 restaurants by randomly selecting three gasoline stations near each restaurant. Historical data was then used to calculate the average annual cost of gasoline. The Restaurant Number, Geographic Region, Annual Revenue, Average Cost of Gasoline, Miles from the Interstate, Square Footage and Annual Increase in Revenue were collected for these 150 restaurants. StatCrunch Data Set: https://www.statcrunch.com/app/?dataurl=http%3A%2F%2Fwww.statcrunch.com%2Fbooks%2FCQL%2F dataset%2FCracker_Barrel.txt&dlim=tab&ft=true Corporate headquarters wants to create a simple linear regression model to predict a restaurant’s annual revenue using the average cost of gasoline.
1. First, create a scatterplot using Average Cost of Gasoline as the independent variable and Annual Revenue as the dependent variable. Does it appear to have a linear association?
2. After performing a visual analysis of the scatterplot, if appropriate, construct a simple linear regression model using the average cost of gasoline to predict a restaurant’s annual revenue.
3. Using your simple linear regression model, what is the value for the slope for this regression model? Interpret the slope in this context.
4. Corporate headquarters is interested in forecasting a restaurant’s annual revenue based upon the average cost of a gallon of gasoline. Using your simple linear regression model, what is the predicted Annual Revenue of a restaurant when the Average Cost of Gasoline is $3.00?
5. Based upon your simple linear regression, should the restaurant chain be concerned if the price of gasoline jumps to $4.00 per gallon? Explain.
