a)
To create: A scatterplot for the data.
Introduction:
b)
To estimate: The regression equation to predict the peak power load.
Introduction: Forecasting is a technique of predicting future events based on historical data and projecting them into the future with a mathematical model. Forecasting may be an intuitive or subjective prediction.
c)
To determine: Whether the estimated equation is adequate.
Introduction: Forecasting is a technique of predicting future events based on historical data and projecting them into the future with a mathematical model. Forecasting may be an intuitive or subjective prediction.
d)
To use: The final equation to predict the peak power load.
Introduction: Forecasting is a technique of predicting future events based on historical data and projecting them into the future with a mathematical model. Forecasting may be an intuitive or subjective prediction.
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Chapter 13 Solutions
Practical Management Science
- Suppose you have invested 25% of your portfolio in four different stocks. The mean and standard deviation of the annual return on each stock are shown in the file P11_46.xlsx. The correlations between the annual returns on the four stocks are also shown in this file. a. What is the probability that your portfolios annual return will exceed 30%? b. What is the probability that your portfolio will lose money during the year?arrow_forwardYou want to take out a 450,000 loan on a 20-year mortgage with end-of-month payments. The annual rate of interest is 3%. Twenty years from now, you will need to make a 50,000 ending balloon payment. Because you expect your income to increase, you want to structure the loan so at the beginning of each year, your monthly payments increase by 2%. a. Determine the amount of each years monthly payment. You should use a lookup table to look up each years monthly payment and to look up the year based on the month (e.g., month 13 is year 2, etc.). b. Suppose payment each month is to be the same, and there is no balloon payment. Show that the monthly payment you can calculate from your spreadsheet matches the value given by the Excel PMT function PMT(0.03/12,240, 450000,0,0).arrow_forwardThe method for rating teams in Example 7.8 is based on actual and predicted point spreads. This method can be biased if some teams run up the score in a few games. An alternative possibility is to base the ratings only on wins and losses. For each game, you observe whether the home team wins. Then from the proposed ratings, you predict whether the home team will win. (You predict the home team will win if the home team advantage plus the home teams rating is greater than the visitor teams rating.) You want the ratings such that the number of predictions that match the actual outcomes is maximized. Try modeling this. Do you run into difficulties? (Remember that Solver doesnt like IF functions.) EXAMPLE 7.8 RATING NFL TEAMS9 We obtained the results of the 256 regular-season NFL games from the 2015 season (the 2016 season was still ongoing as we wrote this) and entered the data into a spreadsheet, shown at the bottom of Figure 7.38. See the file NFL Ratings Finished.xlsx. (Some of these results are hidden in Figure 7.38 to conserve space.) The teams are indexed 1 to 32, as shown at the top of the sheet. For example, team 1 is Arizona, team 2 is Atlanta, and so on. The first game entered (row 6) is team 19 New England versus team 25 Pittsburgh, played at New England. New England won the game by a score of 28 to 21, and the point spread (home team score minus visitor team score) is calculated in column J. A positive point spread in column J means that the home team won; a negative point spread indicates that the visiting team won. The goal is to determine a set of ratings for the 32 NFL teams that most accurately predicts the actual outcomes of the games played.arrow_forward
- Sometimes we wish to analyze the effect of changing a parameter over a wide range of values. Performing changes over a wide range is known as parametric analysis. This can be accomplished by using the sensitivity analysis to establish the range above and below the current value, and then changing the current value to a number outside the current range to find a new range for this parameter. For example, consider the following model: minimize 5X1 + 8X2 subject to (1) 2X1 + 5X2 ≥ 910 (2) 4X1 + 3X2 ≥ 1092 (3) X1 + 9X2 ≥ 819 X1 , X2 ≥ 0 (a) Solve this model graphically. (b) From the graph, perform a sensitivity analysis on b2, the rhsarrow_forwardA small manufacturing firm collected the following data on advertising expenditures A (in thousands of dollars) and total revenue R (in thousands of dollars). (a) Draw a scatter diagram of the data. Comment on the type of relation that may exist between the two variables.(b) The quadratic function of best fit to these data isR(A) = - 7.76A2 + 411.88A + 942.72Use this function to determine the optimal level of advertising.(c) Use the function to predict the total revenue when the optimal level of advertising is spent.(d) Use a graphing utility to verify that the function given in part (b) is the quadratic function of best fit.(e) Use a graphing utility to draw a scatter diagram of the data and then graph the quadratic function of best fit on the scatter diagram.arrow_forward2 Vidhya Balan is planning to liquidate her investments inmutual funds and invest in real estate. Before makingthe change to her investment strategy, Vidhya wants toforecast the price of mutual funds for the next 2 months.She has collected the following data on the average fundprices for the past 10 months.Month Average Fund Price1 55.12 53.83 53.44 52.955 52.156 52.757 52.658 51.59 52.2510 51.7a Using a five-period moving average, forecast theaverage fund price for Period 11.b. Using exponential smoothing with α = 0.3 forecastthe average fund price for Period 11. Assume an initialforecast for Month 2 (F2) as 55.10arrow_forward
- The output distribution form(s) of the input distribution(s) are generally fairly straightforward to predict (s). FALSE OR TRUE!!arrow_forwardA golf club manufacturer is trying to determine how the price of a set of clubs affects the demand for clubs. The file P10_50.xlsx contains the price of a set of clubs and the monthly sales. Assume the only factor influencing monthly sales is price. Fit the following three curves to these data: linear (Y = a + bX), exponential (Y = abX), and multiplicative (Y = aXb). Which equation fits the data best? Interpret your best-fitting equation. Using the best-fitting equation, predict sales during a month in which the price is $470. File data: Price Demand $400 20,000 $420 19,000 $440 17,000 $460 16,000 $500 14,000 $380 22,000 $290 31,000 $340 26,000 $220 41,000 $700 6,000arrow_forwardTime series decomposition seeks to separate the time series (Y) into 4 components: trend (T), cycle (C), seasonal (S), and irregular (I). What is the difference between these components? The model can be additive or multiplicative. When we do use an additive model? When do we use a multiplicative model? We have different ways of showing and projecting trends in a time series. the three most common are moving averages, exponential smoothing and our new friend regression analysis. How might any of these be used? Have you seen any in use?arrow_forward
- Over a two-year period, the Topper Company sold the following numbers of lawnmowers:Month: 1 2 3 4 5 6 7 8 9 10 11 12Sales: 238 220 195 245 345 380 270 220 280 120 110 85Month: 13 14 15 16 17 18 19 20 21 22 23 24Sales: 135 145 185 219 240 420 520 410 380 320 290 240a. In column A input the numbers 1 to 24 representing the months and incolumn B the observed monthly sales. Compute the three-month moving-averageforecast and place this in the third column. Be sure to align your forecast with theperiod for which you are forecasting (the average of sales for months 1, 2, and 3should be placed in row 4; the average of sales for months 2, 3, and 4 in row 5; andso on.) In the fourth column, compute the forecast error for each month in whichyou have obtained a forecast.arrow_forwardFor f(x) = 3 + 7x − 19x^2 + 2x^4, use complete Horner’s algorithm to find (a) the Maclaurin series (Taylor series about x = 0) (b) the Taylor series for this function about x = 2.arrow_forwardLong-Life Insurance developed a linear model to determine the amount of term life insurance a family of four should have, based on the head of the household's current age. The equation is: y = 163 -0.45xwherey = Insurance needed ($000)x = Current age of head of household Calculate the amount of term life insurance you would recommend for a family of four if the head of the household is 53 years old. (Round your answer to 2 decimal places.)arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,