Linear Regression:

Frank's Convenience Marts are located throughout metropolitan Chicago in the United States. Suzanne, the business development manager, plans to open a new store in the Jackson Park neighbourhood in south Chicago. She has found a potential location. To help with the financial analysis, she wants to forecast the daily sales based on data she draws from current stores. Specifically, she selected a random sample of 15 existing stores, and her assistant Nick helped her collect average daily sales, the floor space (area, in square feet) and the median income of families in that ZIP code region for each store. The data is under the worksheet Basic Data in the file Q5_FMC.xlsx.

a) Develop a correlation matrix. What is the correlation between the dependent variable and each of the independent variables? Interpret their managerial implications.

b) Conduct a multiple linear regression using Daily Sales as the dependent variable and Store Area and Area Income as the independent variables. Provide the regression output and write out the regression equation based on this model. Explain the meaning of each of the coefficients. Should all independent variables be included in the model, and why? What is the overall quality of this regression model?

c) Nick reminded Suzanne that the landlord of the potential location mentioned several times that the location has 5 designated parking spaces. Nick then collected parking space information for the 15 sampled stores and the data is provided under the worksheet Parking in Q5_FMC.xlsx. How will this new information change your forecast for the new location?

d) Based on her experience, Suzanne believes that if a store is close to (within a 200-metre radius) to a gas station, the store's sales will be affected. However, the effect depends on whether the neighbouring gas station has a convenience store of its own or not. If not, then a gas station in the proximity should increase sales for the FCM. If yes, then it hurts the sales of the FCM. Now Nick has also collected information about the gas stations (the data is available under the worksheet Gas Station in Q5_FMC.xlsx). Nick then suggests that they should create a new "dummy variable" to capture the impact of the gas station. Specifically, he proposes to assign a value of "0" to the dummy variable if the store is NOT close to a gas station, a value of "1" to the dummy variable, if the store is close to a gas station without a convenience store, and a value of "-1" to the dummy variable if the store is close to a gas station with a convenience store. Do you agree with Nick's approach? Please explain.

e) Can you help Suzanne and Nick to correctly estimate the impact of a gas station? Please carry out the necessary regressions and explain your results. Specifically, what does your result say about Suzanne's earlier hypotheses?

f) Suzanne is wondering if having more parking spaces is more beneficial to larger stores. Can you help Suzanne with her question? Please carefully explain your findings.

Attachment:- q5_fcm.rar