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BIA672

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Marketing

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Jan 9, 2024

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1. An owner of a successful restaurant in Hoboken has decided to open a new restaurant in Washington DC. To find the best location of the new restaurant, the owner has combined the income demographics of Hoboken residents with the income demographics of all the zip codes in Washington in a SAS dataset (“income_byzip_DC_HB” ). To recommend the best zip codes to be considered perform the following analysis. a. Cluster the zip codes in the datasets into six zip codes using hierarchical clustering and average distance and recommend the appropriate zips codes. b. Cluster the zip codes in the datasets into six zip codes using Kmeans and recommend the appropriate zips codes. (20 points) Code: libname sasdata "O:\Marketing_analytics\SAS_data" access=read; run; proc copy in=sasdata out=work; select income_byzip_dc_hb; run; data DC other_states; set income_byzip_dc_hb; if STATEFIPS=11 then output DC; else output other_states; run; proc cluster data = DC outtree=DC_tree method=SINGLE ; var Returns_pct1 Returns_pct2 Returns_pct3 Returns_pct4 Returns_pct5 Returns_pct6; id zipcode; run; proc tree data =DC_tree noprint ncl=6 out=pout_hclust6; copy zipcode; run;

proc print data=pout_hclust6; run; ods rtf file="O:\Marketin_analytics\SAS_output\phclust6.rtf"; proc fastclus data =DC maxclusters =6 out=DC_clusters ; var Returns_pct1 Returns_pct2 Returns_pct3 Returns_pct4 Returns_pct5 Returns_pct6; id zipcode; run; ods rtf close; ods pdf file="O:\Marketin_analytics\SAS_output\phclust6.pdf"; ods pdf close; ods html path="O:\Marketin_analytics\SAS_output\" body="test.html"; ods html close; 2. A beef product retailer is looking to develop a price elasticity model for his product. The prices and sales quantities are stored in the “Beef_price_quantity” SAS dataset. Using regression, develop Price-Quantity and Log-Log models in SAS. Select the best model for the product. Explain your recommendation. (20 points) code: libname sasdata "O:\Marketing_analytics\SAS_data"; proc copy in=sasdata out=work; select beef_price_quantity; run;

data beef_price_quantity_b; set beef_price_quantity; Quantity_ln=log(Quantity); Price_ln=log(Price); run; proc sort data=beef_price_quantity_b; by Price_ln; ods rtf file="O:\BIA672\SAS_output\price.rtf"; run; proc sgplot data=beef_price_quantity_b ; series x=Price_ln y=Quantity_ln; run; proc reg data=beef_price_quantity_b ; model Quantity_ln=Price_ln; run; quit; proc sgplot data=beef_price_quantity_b; series x=Price y=Quantity; run; proc reg data=beef_price_quantity_b; model Quantity=Price; run; ods rtf close;

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3. We have introduced a new feature on our new webpage. To test the effectiveness of the new feature, we have conducted an A/B test and displayed each of the new and old webpages to 2,000 potential customers separately. We would like to know if our new feature is significantly better than the old feature. The result of our analysis is presented in the following table: (10 points) a. Is the new feature better than the old feature? b. Would your answer change if only 650 customers clicked on the webpage? Why or why not? To address your questions, we'll need to analyze the A/B test results statistically. Let's break down each part: a. Is the new feature better than the old feature? To determine if the new feature is better, we can use a hypothesis test. Here, the null hypothesis (H0) is that there is no difference in the effectiveness of the old and new features, while the alternative hypothesis (H1) is that the new feature is more effective. Given the data:  Old Website: 600 clicks out of 2000 visitors  New Website: 675 clicks out of 2000 visitors We'll calculate the click-through rate (CTR) for each and perform a statistical test to see if the difference is significant. The formula for the CTR is: CTR=Number of Clicks/Number of Visitors We can then use a two-proportion z-test to compare the CTRs. b. Would your answer change if only 650 customers clicked on the webpage? Why or why not? If only 650 customers clicked on the webpage, it would imply a different CTR for the new website. We would need to recalculate the statistical significance with the updated numbers. The change in the number of clicks can impact the p-value and might lead to a different conclusion about the effectiveness of the new feature. CODE: First Name : shashank • Last Name :Arshanapally

• Program: A/B Testing Analysis • Purpose: A/B testing for webpage feature effectiveness ******************************************************************/ data click_data; input feature $ clicked $ count; datalines; Old yes 600 Old no 1400 New yes 675 New no 1325 ; run; proc freq order=data data=click_data; weight Count; table feature*clicked / chisq riskdiff; run; /** Adjusting A/B testing analysis parameters for the current scenario **/ proc power; title "Sample Size Calculation for Traditional A/B Testing"; twosamplefreq TEST=pchi /** Updating these values based on your specific A/B testing scenario **/ /** Example values below - these should be updated based on your actual scenario **/ proportiondiff = .03375 /** Difference in proportions from your A/B test **/ refproportion = .03 /** Reference proportion from the old webpage **/ npergroup = 2000 /** Number of visitors per group in your A/B test **/ power = 0.80 /** Desired power level **/ alpha = 0.05; /** Significance level **/ run; 4. What sample size would you choose to conduct a test that could detect a 3% difference from a 20% click rate? Assume beta=20 and alpha=.05. Code: ****************************************************************** • First Name shashank

• Last Name arshanapally • Program: • Purpose: A/B Testing ******************************************************************/ /* Existing Data Input and Analysis */ data click_data; input feature $ clicked $ count; datalines; Old yes 300 Old no 700 New yes 345 New no 655 ; run; proc freq order=data data=click_data; weight Count; table feature * clicked / chisq riskdiff; run; /* A/B Testing Sample Size Calculation for 3% Difference from 20% Click Rate */ proc power; title "Sample Size Calculation for Detecting 3% Difference from 20% Click Rate"; twosamplefreq TEST=pchi proportiondiff = 0.03 /* 3% difference to detect */ refproportion = 0.20 /* Reference proportion (20% click rate) */ npergroup = . power = 0.80 /* 80% power, corresponds to beta of 20% */ alpha = 0.05; /* 5% significance level */ run;

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5. A marketer of a product is willing to invest in the acquisition of new customers for two years. What would be the upper limit of this investment, per customer, assuming the following retention/attrition rates (see table below) and assumptions? Should the marketer spend an additional $7.00 per month to increase the retention rate by 1% per month (e.g., 97 instead of 96 or 76 instead of 75)? (20 points) Assumptions: o Revenue per customer per month=$250 o Payments are made at the end of the month o Annual internal rate of return of 18% compounded monthly Answer in Excel file 6 c. Both customers and non-customers 7 c. Healthy eating 8 b. Soccer Moms 9 b. University of Virginia 10 c. Mid-range 11 d. Low quality 12 d. Through third-party distributors 13 b. 10 to 20 14 c. New Hampshire and Pennsylvania 15. C. Swedish

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