Question

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 travelling 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. Corporate headquarters wants to create a simple linear regression model to predict a​ restaurant's annual revenue using the average cost of gasoline. First create a scatterplot using Average Cost of Gasoline as the independent variable and Annual Revenue as the dependent variable. 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. What is the correlation coefficient between Average Cost of Gasoline and Annual​ Revenue?

Answer 1