Question: Again working with the ‘New Restaurant’ dataset (available as an Excel spreadsheet or SPSS data file, “Exam2_new-restaurant”), explore how well the number of customers a restaurant has on opening day (‘Customers’) predicts the profit of the restaurant in the first 6 months (‘Profit’). Your key research question is: Does the number of customers a restaurant has on opening day significantly predict the profit of the restaurant in the first 6 months? (20 points)

a) What is the null and alternative hypothesis? (1 point)

b) Produce box plots for the two variables of interest and a scatterplot with customers on the x-axis and profit on the y-axis. Interpret these plots with regards to the key assumptions of regression these plots address. (4 points)

c) Report and interpret r and r². (4 points)

d) Write the regression equation for profit (y) regressed on customers (x). Interpret the slope and intercept. What is the predicted profit for a restaurant that had 30 customers on day 1? (4 points)

e) What is the 95% confidence interval for the slope? Interpret this interval. (2 points)

f) What do you conclude with regards to your hypothesis? Report the relevant test statistic(s) and p-value(s) to support your conclusion. What is the ‘take home message’ for people hoping to open a new restaurant? (5 points)