Ten weeks of data on the Commodity Futures Index are:7.35 7.40 7.55 7.56 7.60 7.52 7.52 7.70 7.62 7.55 a. Construct a time series plot. What type of pattern exists in the data?b. Use trial and error to find a value of the exponential smoothing coefficient a thatresults in a relatively small MSE.
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Ten weeks of data on the Commodity Futures Index are:
7.35 7.40 7.55 7.56 7.60 7.52 7.52 7.70 7.62 7.55
a. Construct a time series plot. What type of pattern exists in the data?
b. Use trial and error to find a value of the exponential smoothing coefficient a that
results in a relatively small MSE.
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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?A small computer chip manufacturer wants to forecast monthly ozperating costs as a function of the number of units produced during a month. The company has collected the 16 months of data in the file P13_34.xlsx. a. Determine an equation that can be used to predict monthly production costs from units produced. Are there any outliers? b. How could the regression line obtained in part a be used to determine whether the company was efficient or inefficient during any particular month?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.
- The file P13_26.xlsx contains the monthly number of airline tickets sold by the CareFree Travel Agency. a. Create a time series chart of the data. Based on what you see, which of the exponential smoothing models do you think will provide the best forecasting model? Why? b. Use simple exponential smoothing to forecast these data, using a smoothing constant of 0.1. c. Repeat part b, but search for the smoothing constant that makes RMSE as small as possible. Does it make much of an improvement over the model in part b?The management of a technology company is trying to determine the variable that best explains the variation of employee salaries using a sample of 52 full-time employees; see the file P13_08.xlsx. Estimate simple linear regression equations to identify which of the following has the strongest linear relationship with annual salary: the employees gender, age, number of years of relevant work experience prior to employment at the company, number of years of employment at the company, or number of years of post secondary education. Provide support for your conclusion.Stock market analysts are continually looking for reliable predictors of stock prices. Consider the problem of modeling the price per share of electric utility stocks (Y). Two variables thought to influence this stock price are return on average equity (X1) and annual dividend rate (X2). The stock price, returns on equity, and dividend rates on a randomly selected day for 16 electric utility stocks are provided in the file P13_15.xlsx. Estimate a multiple regression equation using the given data. Interpret each of the estimated regression coefficients. Also, interpret the standard error of estimate and the R-square value for these data.
- The file P13_42.xlsx contains monthly data on consumer revolving credit (in millions of dollars) through credit unions. a. Use these data to forecast consumer revolving credit through credit unions for the next 12 months. Do it in two ways. First, fit an exponential trend to the series. Second, use Holts method with optimized smoothing constants. b. Which of these two methods appears to provide the best forecasts? Answer by comparing their MAPE values.The file P13_28.xlsx contains monthly retail sales of U.S. liquor stores. a. Is seasonality present in these data? If so, characterize the seasonality pattern. b. Use Winters method to forecast this series with smoothing constants = = 0.1 and = 0.3. Does the forecast series seem to track the seasonal pattern well? What are your forecasts for the next 12 months?Macomb Inc. used Excel to run a least-squares regression analysis on the production cost data resulting in the following output: Regression StatisticsMultiple R 0.9834 R Square 0.9596 Observations 30 Coefficients Standard Error T Stat P-ValueIntercept 174,980 61,580 2.84 0.021 Production units (X) 11.53 0.9265 12.44 0.000 What total cost would Macomb predict for a month in which production is 2,000 units? Multiple Choice $174,900 $63,433 $198,040 $23,037
- 1.) Use the following dummy variables to develop an estimated regression equation to account for seasonal effects only in the data. Qtr1 = 1 if Quarter 1, 0otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise, Qtr3 = 1 if Quarter 3, 0otherwise. Based only on the seasonal effects in the data, compute estimates of quarterly sales for year 6.a. Report the estimate of sales for Year 6 Quarter 1. (Enter a whole value.)b. Report the estimate of sales for Year 6 Quarter 4. (Enter a whole value.)2.) Let Period t = 1 refer to the observation in quarter 1 of year 1; Period t = 2refer to the observation in quarter 2 or year 1; … and Period t = 20 refer to the observation in quarter 4 of year 5. Using the dummy variables defined in part (b) and Period (t), develop an estimated regression equation to account for seasonal effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute the estimates of quarterly sales for year 6.a. Report the estimate…Home-Style Cookies tracks monthly sales by type of cookie, see the following table. Month Chocolate Chip (000 units) Peanut Butter (000 units) Filled (000 units) Feb. 19 15 10 Mar. 18 14 9 Apr. 15 11 8 May 20 16 11 Jun. 18 14 10 Jul. 22 18 12 Aug. 20 16 10 Sep. Create a line chart in Excel showing monthly sales by type of cookies (each type will have its own line); then, forecast September sales volume for chocolate chip cookies using each of the following: the naïve approach; a 5-month moving average; a weighted average using .60 for August, .30 for July, and .10 for June; and a linear trend equation.Consider the following time series. t 1 2 3 4 5 yt 6 11 9 14 15 (a) Choose the correct time series plot. (i) (ii) (iii) (iv) What type of pattern exists in the data? (b) Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. If required, round your answers to two decimal places. y-intercept, b0 = Slope, b1 = MSE = (c) What is the forecast for t = 6? If required, round your answer to one decimal place.