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- The owner of a restaurant in Bloomington, Indiana, has recorded sales data for the past 19 years. He has also recorded data on potentially relevant variables. The data are listed in the file P13_17.xlsx. a. Estimate a simple regression equation involving annual sales (the dependent variable) and the size of the population residing within 10 miles of the restaurant (the explanatory variable). Interpret R-square for this regression. b. Add another explanatory variableannual advertising expendituresto the regression equation in part a. Estimate and interpret this expanded equation. How does the R-square value for this multiple regression equation compare to that of the simple regression equation estimated in part a? Explain any difference between the two R-square values. How can you use the adjusted R-squares for a comparison of the two equations? c. Add one more explanatory variable to the multiple regression equation estimated in part b. In particular, estimate and interpret the coefficients of a multiple regression equation that includes the previous years advertising expenditure. How does the inclusion of this third explanatory variable affect the R-square, compared to the corresponding values for the equation of part b? Explain any changes in this value. What does the adjusted R-square for the new equation tell you?Suppose that a regional express delivery service company wants to estimate the cost of shipping a package (Y) as a function of cargo type, where cargo type includes the following possibilities: fragile, semifragile, and durable. Costs for 15 randomly chosen packages of approximately the same weight and same distance shipped, but of different cargo types, are provided in the file P13_16.xlsx. a. Estimate a regression equation using the given sample data, and interpret the estimated regression coefficients. b. According to the estimated regression equation, which cargo type is the most costly to ship? Which cargo type is the least costly to ship? c. How well does the estimated equation fit the given sample data? How might the fit be improved? d. Given the estimated regression equation, predict the cost of shipping a package with semifragile cargo.Dilberts Department Store is trying to determine how many Hanson T-shirts to order. Currently the shirts are sold for 21, but at later dates the shirts will be offered at a 10% discount, then a 20% discount, then a 40% discount, then a 50% discount, and finally a 60% discount. Demand at the full price of 21 is believed to be normally distributed with mean 1800 and standard deviation 360. Demand at various discounts is assumed to be a multiple of full-price demand. These multiples, for discounts of 10%, 20%, 40%, 50%, and 60% are, respectively, 0.4, 0.7, 1.1, 2, and 50. For example, if full-price demand is 2500, then at a 10% discount customers would be willing to buy 1000 T-shirts. The unit cost of purchasing T-shirts depends on the number of T-shirts ordered, as shown in the file P10_36.xlsx. Use simulation to determine how many T-shirts the company should order. Model the problem so that the company first orders some quantity of T-shirts, then discounts deeper and deeper, as necessary, to sell all of the shirts.
- .A 45 kW rated solar power system has its power output and the Solar irradiance on the PV system measured during daylight hours over a day. Based on the following data, create a scatter plot of the power output of the PV system vs the solar irradiance and comment on the relationship between the two. Based on the data, can you tell which season this day was in? Solar Irradiance on the PV system (kW/m²) 0 0.079 0.333 0.571 0.751 0.86 0.914 0.93 0.904 0.803 0.606 0.345 0.054 Power output from the PV system (kW) 0 3.098 12.438 20.124 25.703 28.498 29.587 29.69 28.798 26.264 20.434 12.223 2Use the below formula to calculate the CLV for the following: A manager of a cable company wants to determine if it is strategic to acquire the Brett family, by estimating their household-level CLV. The manager estimates that it will cost the company $80 (A) to get the Bretts’ to switch, and the Bretts’ will generate $150 profit each year (M), with a $30 annual marketing cost to retain them (C). The estimated retention rate (r) is 65%, and the current discount rate is 5%.(d) i) CLV= ii) Based on your calculation, are the Brett’s profitable to the cable company?The manager of the local National Video Store sells videocassette recorders at discount prices. If the store does not have a video recorder in stock when a customer wants to buy one, it will lose the sale because the customer will purchase a recorder from one of the many local competitors. The problem is that the cost of renting warehouse space to keep enough recorders in inventory to meet all demand is excessively high. The manager has determined that if 90% of customer demand for recorders can be met, then the combined cost of lost sales and inventory will be minimized. The manager has estimated that monthly demand for recorders is normally distributed, with a mean of 180 recorders and a standard deviation of 60. Determine the number of recorders the manager should order each month to meet 90% of customer demand.
- Jon is preparing a newsletter to his clients. As part of his newsletter, he reports their economic outlook for the coming year. He samples 85 of his clients, and they report that they expect to hire 7.8 new employees during the coming year. Last year all of his clients averaged 6.3 hires with a standard deviation of 4.0. Jon wants to know if the expected number of new hires has significantly increased at the 5% significance level. What are the null and alternate hypotheses?For the E-Commerce Retail Sales (Million$) data given in the table below, provide estimates from the 1st Quarter (Q1) of 2016 to the 3rd Quarter (Q3) of 2017 by using two models: 1) Single Exponential Smoothing with α=0.3 2) Moving Average with k=2. Calculate MAPE for each model. Quarter Year Actual Q1 2016 86802 Q2 2016 92004 Q3 2016 93795 Q4 2016 124651 Q1 2017 99491 Q2 2017 106590 Q3 2017 108291 Compare two models above (Single Exponential Smoothing and Moving Average) based on their accuracies. Which forecasting method appears to be better? Using the model you choose, provide forecast for the 4th Quarter (Q4) of 2017. Assuming that this model is overestimating, find the actual value of the Q4 of 2017 based on MAPE value. Some residual graphs from the first forecast model (including wider range of E-Commerce Retail Sales data) are given below. What do these graphs tell about the model? Explain each graph.Emenyi Company Limited is considering using Markov analysis to analyze brand switching between three different brands of its Detox medicated soap; Detox White, Detox Green and Detox Orange. The company’s marketing specialist conducted a survey and gathered data which she utilized to estimate the following transition matrix. The matrix shows the probability of moving between brands each month: From White Green OrangeWhite 0.78 0.11 0.11 Green 0.04 0.94 0.02 Orange 0.20 0.04 0.76 The current (month 1) market shares are 50%, 20% and 30% for Detox White, Detox Green and Detox Orange respectively. Required (i) What will be the expected market shares for each of the three brands after two months have elapsed (that is, in month 3)?(ii) What is the long-run prediction for the expected market share for each of the three brands?
- The following table gives the number of pints of type A blood used at Damascus Hospital in the past 6 weeks: Week of Pints Used August 31 360 September 7 370 September 14 412 September 21 383 September 28 371 October 5 371 a) The forecasted demand for the week of October 12 using a 3-week moving average= {__] Pints (round your response to two decimal places).4. A credit rating company recommends granting of credit cards based on several criteria. One is annual income. If the annual income of applicants is normally dis- tributed with mean $22,000 and standard deviation $4,800 and the company recommends no applicant unless his or her income exceeds $15,000, what fraction of the applicants are denied on this basis?An operation analyst is forecasting this year's demand for one of his company's products based on the following historical data: (4 year ago Quantity sold was 10842), (3 year ago Quantity sold was 11881 ), (2 year ago Quantity sold was 16064 ) and the last year Quantity sold was 19273 . The previous trend line had predicted 12250 for three years ago, 13000 for two years ago and 13750 for last year. What was the mean absolute percent error (MAPE) for these forecasts? a. 16.95 b. 2739 c. 0.17 d. 2985