Café Michigan's manager, Gary Stark, suspects that demand for mocha latte coffees depends on the price being charged. Based on historical observations, Gary has gathered the following data, which show the numbers of these coffees sold over six different price values: Price $2.60 Number Sold 760 $3.40 510 $1.90 990 $4.20 250 $3.10 320 $4.10 490 Using simple linear regression and given that the price per cup is $1.85, the forecasted demand for mocha latte coffees will be (enter your response rounded to one decimal place). cups
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- Regression analysis. The owner of a small hardware store has noted a sales pattern for window locks Problem 6that seems to parallel the number of break-ins reported each week in the newspaper. The data are:Sales: 46 18 20 22 27 34 14 37 30Break-ins: 9 3 3 5 4 7 2 6 4a. Plot the data to determine which type of equation, linear or nonlinear, is appropriate.b. Obtain a regression equation for the data.c. Estimate average sales when the number of break-ins is five.For the Restaurant Sales database,:(a) Obtain the Min and Max amount in sales(b) For each Bin shown in the excel sheet, calculate the frequency for each bin as follows:For ex: if the Bin value is $200, the frequency is the number of entries, whose sales are Less than or equal to 200.Next Bin value is $250 => Frequency is the number of entries, whose sales is >200 and less than or equal to 250.And so on…. (c) Now that your values for Frequency and Bins is complete, use any data visualization tool/chart to plot – Sales on the X axis and Frequency on Y axis.(d) Looking at the plot /graph/chart in (c), what do you infer about the relationship?Cafe X is selling coffee in three different sizes at the prices and costs shown in the first table below. As shown in the second table, they are considering raising the price of their small to $2.75, and they project that sales of smalls will go down while sales of mediums and larges will go up slightly. Fill out the tables below to calculate the projected change in gross margin based on the estimated changes in cups sold. You may find it helpful to use a spreadsheet for the calculations. Increased Price for Small Coffee Small 0 Large Price per Cup Total Cost per Cup Est. Change in Cups Sold with Small @ $2.75 Medium $3.50 $0.35 +6% $2.75 $0.20 -10% $4.50 $0.50 +3% Cups Sold 0 0 0 $ 0 $ Revenue 0 $ 0 $ 0 $ 0 $ 0 $ 0 $ 0 COGS Change in Gross Margin (positive number for increase, negative for decrease): $ $ 0 $ 0 $ 0 $ Gross Margin 0 ▾
- A marketing professor at Givens College is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 156 students who took the course last semester are provided in the tile MktHrsPts. Develop a scatter chart for these data. What does the scatter chart indicate about the relationship between total points earned and hours spent studying? Develop an estimated regression equation showing how total points earned is related to hours spent studying. What is the estimated regression model? Test whether each of the regression parameters β0 and β1 is equal to zero at a 0.01 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable? How much of the variation in the sample values of total point earned does the model you estimated in part (b) explain? Mark Sweeney spent 95 hours studying. Use the regression model you estimated in part (b) to predict the total points Mark earned.Suppose a baker wants to know, on average, how many pastries they sell in a day. They sampled over 4 days. On the first day they sold 10, on the second day they sold 12, on the third day they sold 18, and on the fourth day they sold 16. The population standard deviation of pastry sales is 3. What is the point estimate (average) number of pastries sold? 26 08 056 O 14 NexThe controller for Dohini Manufacturing Company felt that the number of purchase orders alone did not explain the monthly purchasing cost. He knew that nonstandard orders (for example, one requiring an overseas supplier) took more time and effort. He collected data on the number of nonstandard orders for the past 12 months and added that information to the data on purchasing cost and total number of purchase orders. Multiple regression was run on the above data; the coefficients shown by the regression program are: Required: 1. Construct the cost formula for the purchasing activity showing the fixed cost and the variable rate. 2. If Dohini Manufacturing Company estimates that next month will have 430 total purchase orders and 45 nonstandard orders, what is the total estimated purchasing cost for that month? (Round your answer to the nearest dollar.) 3. What if Dohini Manufacturing wants to estimate purchasing cost for the coming year and expects 5,340 purchase orders and 580 nonstandard orders? What will estimated total purchasing cost be? What is the total fixed purchasing cost? Why doesnt it equal the fixed cost calculated in Requirement 2? (Round your answers to the nearest dollar.)
- Curry Rubber manufactures rubber bands for retail companies. The accounting manager has performed a regression analysis of past data. You notice that the formula has an R-squared of 0.68, a t-value of 2.2, and a standard error of the estimate of $218,200. The estimate for next quarter costs is $2,597,623. Calculate Standard Error as a % of predicted total cost which represents a measure of precision of his regression analysis? (Round your answer to one decimal place, i.e., 0.052 = 5.2%.)The Paymore Rental Car Agency rents cars in a small town. It wants to determine how many rental cars it should maintain. Based on market projections and historical data, the manager has determined probability distributions for the number of rentals per day and rental duration (in days only) as shown in the following tables: Number of customers per day Probability 0 .20 1 .20 2 .50 3 .10 Rental duration in days Probability 1 .10 2 .30 3 .40 4 .10 5 .10 Design a simulation experiment for the car agency and simulate using a fleet of four rental cars for 10 days. Compute the probability that the agency will not have a car available upon demand. Should the agency expand its fleet? Explain how a simulation experiment could be designed to determine the optimal fleet size for the Paymore Agency. Use the following random numbers in order (from left to right) for the simulation of number of customers per day: 0.62 0.48 0.96 0.86 0.86 0.29 0.79 0.22 0.08 0.62…The following time series shows the sales of a particular product over the past 12 months. Construct a time series plot. What type of pattern exists in the data? Use α = 0.3 to compute the exponential smoothing values for the time series. Use trial and error to find a value of the exponential smoothing coefficient α that results in a relatively small MSE.
- Duke Energy reported that the cost of electricity for an efficient home in a particular neighborhood of Cincinnati, Ohio, was $104 per month. A researcher believes that the cost of electricity for a comparable neighborhood in Chicago, Illinois, is higher. A sample of homes in this Chicago neighborhood will be taken and the sample mean monthly cost of electricity will be used to test the following null and alternative hypotheses. Assume the sample data lead to rejection of the null hypothesis. What would be your conclusion about the cost of electricity in the Chicago neighborhood? What is the Type I error in this situation? What are the consequences of making this error? What is the Type II error in this situation? What are the consequences of making this error?Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in several markets in the southern United States. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow: a. Develop an estimated regression equation with the amount of television advertising as the independent variable. Test for a significant relationship between television advertising and weekly gross revenue at the 0.05 level of significance. What is the interpretation of this relationship? b. How much of the variation in the sample values of weekly gross revenue does the model in part (a) explain? c. Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. Test whether each of the regression parameters 0, 1, and 2 is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable? d. How much of the variation in the sample values of weekly gross revenue does the model in part (c) explain? e. Given the results in parts (a) and (c), what should your next step be? Explain. f. What are the managerial implications of these results?An entrepreneur runs a website that sells car tires online. Based on the Regression output below, how much in Advertising Budget do you predict is needed to sell 40 tires per day. (round to the nearest dollar) SUMMARY OUTPUT Regression Statistics Multiple R 0.93303 R Square 0.87055 Adjusted R Square 0.85616 Standard Error 4.91656 Observations 11 P-Value Standard Error Coefficients Intercept 12.5671 3.16973 0.0032807 Advertising Budget 0.07224 009286 0.0000277 O $380 $107 O $15 O $50 O $192