24 Develop a multiple regression model of the form using the following data to predict y from x. From a scatter plot and Tukey's ladder of transformation, explore ways to recode the data and develop an alternative regression model. Compare the results. Appendix A Statistical Tables y 2,485 1,790 874 2,190 3,610 2,847 1,350 x 3.87 3.22 2.91 3.42 3.55 3.61 3.13 y 740 4,010 3,629 8,010 7,047 5,680 1,740 x 2.83 3.62 3.52 3.92 3.86 3.75 3.19 (Round your answers to 4 decimal places.) logy = + x Click if you would like to Show Work for this question: Question 25 Study the output given here from a stepwise multiple regression analysis to predict y from four variables. Comment on the output at each step. Appendix A Statistical Tables Number of steps = (Round the coefficients 1,2,3,4 to 2 decimal places, round the coefficient 5 to 4 decimal places.) Regression model at the last step: + + + + Click if you would like to Show Work for this question: Open Show Work Question 26 The "Economic Report to the President of the United States" included data on the amounts of manufacturers new and unfilled orders in millions of dollars. Shown here are the figures for new orders over a 21-year period. Use a computer to develop a regression model to fit the trend effects for these data. Use a linear model and then try a quadratic model. How well does either model fit the data? Year Total Number of New Orders 1 2 3 4 5 6 7 8 9 10 55,022 55,921 64,182 76,003 87,327 85,139 99,513 115,109 131,629 147,604 11 156,359 Year *(Round your answers to the nearest integer.) **(Round your answer to 1 decimal place.) = *+( *) Period = *+( *) Period + ( **) Period2 12 13 14 15 16 17 18 19 20 21 Total Number of New Orders 168,025 162,140 175,451 192,879 195,706 195,204 209,389 227,025 240,758 243,643 The regression trend model is superior, the period2 variable a significant addition to the model. Click if you would like to Show Work for this question:Open Show Work Question 27 Current Construction Reports from the U.S. Census Bureau contain data on new privately owned housing units. Data on new privately owned housing units (1000s) built in the West between 1980 and 2010 follow. Use these time-series data to develop an autoregression model with a one-period lag. Now try an autoregression model with a two-period lag. Discuss the results and compare the two models. Year Housing Starts (1000) 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 318.9 251.3 224.1 390.4 457.3 483.9 509.7 406.0 415.6 402.1 324.9 247.9 268.6 288.2 342.4 1995 328.5 Year Housing Starts (1000) 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 347.4 363.5 401.2 404.3 401.5 413.0 430.9 486.5 541.9 558.6 455.2 343.9 196.7 116.7 128.3 *(Round your answer to 1 decimal places.) **(Round your answer to 2 decimal places.) ***(Round your answer to 3 decimal place.) ****(Round your answer to the nearest integer.) The model with a 1 - period lag: Housing Starts = *+ ** lag 1 F= ** p = *** R2 = *% adjusted R2 = *% se = ** The model with 2 - period lag: Housing Starts = **** + ** lag 2 F= ** p = *** R2 = *% adjusted R2 = *% se = ** The model with is better model with a R2. The model with is . Click if you would like to Show Work for this question: Question 28 The following data contain the quantity (million pounds) of U.S. domestic fish caught annually over a 25-year period as published by the National Oceanic and Atmospheric Administration. a. Use a 3-year moving average to forecast the quantity of fish for the years 1989 through 2010 for these data. Compute the error of each forecast and then determine the mean absolute deviation of error for the forecast. b. Use exponential smoothing and to forecast the data from 1989 through 2010. Let the forecast for 1987 equal the actual value for 1986. Compute the error of each forecast and then determine the mean absolute deviation of error for the forecast. c. Compare the results obtained in parts (a) and (b) using MAD. Which technique seems to perform better? Why? Year Quantity 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 6,137 7,019 7,391 8,750 9,816 9,644 9,951 9,971 10,089 9,693 9,380 1997 9,615 1998 8,992 1999 9,089 Year Quantity 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 8,876 9,290 9,250 9,315 9,424 9,379 9,180 9,026 7,953 7,875 7,994 (Round your answers to 2 decimal place.) a. MADmoving average : b. MAD = .2 : c. The produced a smaller MAD than did . Using MAD as the criterion, was a better forecasting tool than the . \f