Fit a linear trend curve by the least-squares method to the following data and determine trend values and then estimate levels of production in 2010 and 2025. Year 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 Production (M Tons) 12 16 20 24 26 30 34 40 44 48 55
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Fit a linear trend curve by the least-squares method to the following data and determine trend values and then estimate levels of production in 2010 and 2025.
|
Year |
2011 |
2012 |
2013 |
2014 |
2015 |
2016 |
2017 |
2018 |
2019 |
2020 |
2021 |
|
Production (M Tons) |
12 |
16 |
20 |
24 |
26 |
30 |
34 |
40 |
44 |
48 |
55 |
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- Under what conditions might a firm use multiple forecasting methods?The Baker Company wants to develop a budget to predict how overhead costs vary with activity levels. Management is trying to decide whether direct labor hours (DLH) or units produced is the better measure of activity for the firm. Monthly data for the preceding 24 months appear in the file P13_40.xlsx. Use regression analysis to determine which measure, DLH or Units (or both), should be used for the budget. How would the regression equation be used to obtain the budget for the firms overhead costs?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?
- 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.Using linear regression analysis, what would you estimate demand to be for each month next year? Month Forecast January February March April May June July August September October November DecemberThe number of patients coming to the Healthy Start Maternity clinic has been increasing steadilyover the past eight months. You are provided with some historical data as follows: Month Clinic attendance (in thousands)1 3.42 3.93 4.54 5.05 5.86 5.97 6.58 6.7 a. Identify and give a brief explanation of the:i. Dependent variableii. Independent variable b. Use simple linear regression to forecast annual demand for months 9 and 10 by using thetabular method to:i. Derive the values for the intercept and slope. ii. Derive the linear regression equation. iii. Plot the linear regression line. iv. Develop a forecast of the clinic attendance for months 9 and 10.
- Sales of Volkswagen's popular Beetle have grown steadily at auto dealerships in Nevada during the past 5 years (see table below). Year 1 2 3 4 5 Sales 460 502 520 575 575 a) Forecasted sales for year 6 using the trend projection (linear regression) method are sales (round your response to one decimal place).asap!! The product of steel scrap from 1968-77 is given below: Year 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 Production (1000 tons) 3255 3793 3976 3925 4122 4529 4903 3879 4251 4539 Fit a linear trend equation by the method of least squares. Determine the predicted value of trend for 1982 and 1985.The number of cases of merlot wine sold by the Connor Owen winery in an eight-year period is as follows: YEAR CASES OFMERLOT WINE 2005 321 2006 407 2007 449 2008 507 2009 409 2010 551 2011 461 2012 427 Using an exponential smoothing model with an alpha value of 0.30, estimate the smoothed value calculated as of the end of 2012. Use the average demand for 2005 through 2007 as your initial forecast for 2008, and then smooth the forecast forward to 2012.
- 3) Seasonality: The following data represent dinner sales at a busy restaurant. Use linear regression to predict sales for each day of week 5 and the total sales for week 5. Estimate the percentage of weekly sales that occur over the weekend (include Friday, Saturday, and Sunday). Finally, determine which days of the week are increasing and decreasing in sales, using the slopes of the LR lines. Week Mon Wed Fri Sat Sun Tue 177 170 Thu 190 Total 270 152 180 321 386 166 218 203 402 427 167 333 357 229 3 158 170 170 205 163 173 158 225 349 433 212 a) Graph the seasonal data and attach the graph to this page. b) Determine the slope for each day of the week. Mon Tue Wed Thu Fri Sat Sun Total Slope c) Estimate the percentage of weekend sales in week 5: d) For which day are sales increasing the fastest? e) For which day are sales decreasing the fastest?Can you please demonstrate #7 how to identify the coefficient? Given: Year Demand 1 7 2 9 3 5 4 9 5 Predict the value for Year 5: 2 year moving average What is MSE for 2 year moving average? 2 year moving average using 0.6 (weight for the oldest period) and 0.4(weight for most recent period Exponential smoothing, =0.2 and forecast for Year 1 = 5 Linear trend Which forecast method has the least amount of error using MAD? What is the coefficient?A cosmetics manufacturer's marketing department has developed a linear trend equation th its popular Hand & Foot Cream. F = 95,000 + 15,000t Where F = Annual sales t is in years (Enter all answers as whole numbers.) a. Are annual sales increasing or decreasing? By how much? Annual sales are by bottles per year. b. Predict annual sales for year 8 using the equation. Annual sales for year 8 bottles
