The purpose of this case is to apply what you've learned about statistical analysis to a decision-making challenge faced by EuroPet marketing managers: should we cut our convenience store advertising spending? EuroPet is a multinational company operating gasoline stations in Europe, some of which also have convenience stores ("c-stores"). The case presents c-store sales and advertising data for the Marseille market in France. The goal of the analysis was stated bluntly by EuroPet marketing executive Emily Tyler, "...give me proof that our advertising has actually boosted c-store sales and that the increase justifies the advertising spend." Your analysis will be used to help EuroPet assess the impact of advertising on EuroPet c-store sales and decide whether to cut the advertising budget. Please answer the following questions. Copy and paste SPSS output with each answer. Make sure you discuss specific numbers from the SPSS results as part of every answer. Use the data set in file "EuroPet.sav" posted on Canvas, and use significance level = .05 for hypothesis testing. 1. Begin your analysis by calculating descriptive statistics for c-store sales and variables that might be associated with sales. These include: sales, tv, radio, fvolume, fprice, temp, prec, holiday. Summarize all the descriptive statistics in table format (mean, standard deviation, median, mode, minimum, maximum; frequencies for "holiday"). Very briefly discuss only the c-store sales and advertising results (i.e., sales, tv, radio). Take note of the mean, median, and mode for each advertising variable. Note: GRP ("Gross Rating Point") is a commonly used measure of advertising exposure. It is calculated as a percent of the target audience reached multiplied by the exposure frequency. For example, if you reach 30% of the target audience with 4 exposures to the advertising, you would have 120 GRP. Therefore, a GRP=0 indicates no advertising exposure. 2. EuroPet management is interested in whether c-store sales are affected by holidays, and whether advertising levels are higher or lower during holidays. Run three independent sample t-tests to examine this for EuroPet. a. Do average sales increase or decrease on holiday weeks? b. Did EuroPet advertise on TV more or less during holiday weeks? c. Did EuroPet advertise on Radio more or less during holiday weeks? Interpret the results of each t-test. Discuss specific numbers. Based on these three tests, what can you conclude so far about the relationship between holidays and sales and advertising? 3. EuroPet management is interested most in the effects of advertising on c-store sales. Create two scatterplots to get a first look at the relationship between advertising and c-store sales: a. A scatter plot of sales (Y) vs. tv (X) b. A scatter plot of sales (Y) vs. radio (X) Does there appear to be any linear relationship between sales and advertising? (2) 4. Calculate the correlation between c-store sales and variables that might be associated with sales. These include: sales, tv, radio, fvolume, fprice, temp, prec (i.e., a 7x7 correlation matrix). Very briefly describe the correlations/relationships between c-store sales and the other 6 variables. Discuss specific numbers in your answer. [Note: you do not need to analyze every correlation in the matrix; just these six.] 5. Perform a multiple linear regression with c-store sales as the dependent variable (Y) and these independent variables: tv (X1), radio (X2), fprice (X3), temp (X4), prec (X5), holiday (X6): Y = 0 + 1X1 + 2X2 + 3X3 + 4X4 + 5X5 + 6X6 + . a. How well does the model explain variation in c-store sales (i.e., discuss R2 and its meaning for this regression model)? Discuss specific numbers in your answer. b. Use the F-test to assess overall model fit. Is the overall model fit statistically significant? Discuss specific numbers (i.e., the p-value) in your answer. c. Report the estimated coefficient values for each independent variable, include whether each is significantly different from zero (i.e., t-test of H0: =0), and interpret each coefficient value's meaning. Discuss specific numbers in your answer. d. How much are c-store sales predicted to increase or decrease if TV advertising increased by 10 GRP's? Show how you calculated the specific numbers in your answer. 6. Calculate the net impact of c-store advertising on profitability by doing the following: a. One of the two advertising variables from the regression in #5 can be dropped because it is not statistically significant. Identify that variable, drop it, and re-run the regression without it. b. Use your new regression model results (i.e., the advertising regression coefficient) and the following table as a template for calculating the net impact of advertising on profitability. Is c-store advertising profitable? Should advertising spending be cut? Discuss and justify your answer using specific numbers from your profit analysis and relevant results from questions #1-5. Cost of advertising per GRP per week in Marseille (see case page 6)a Short-term increase in sales per GRP for one store (regression coefficient) Multiplication factor for long-term effect of advertising ("mf" from page 4) Long-term increase in sales per GRP (short-term increase per GRP "mf") Overall profit per GRP generated for one c-store (long-term increase in sales 30% profit margin) Total overall profit per GRP generated for all 100 stores (overall profit generated per store 100 stores) Net impact of c-store advertising for all 100 stores (total overall profit per GRP - cost of advertising per GRP) a The cost of advertising per GRP is for the entire Marseilles market, not just for a single store.