Exam 11: Forecasting Models

The data below represents demand,selling price,and advertising expenditures for an electronics item. a.Develop a multiple regression model to predict monthly demand. b.What is the R-squared on this model? c.Based on the model developed in part a,what would be the predicted monthly demand if the price of the item is set to $49 and $100 is spent on advertising?

A multiple regression model may include one or more dependent variables.

Use this information to answer the following questions. The following time series,provided by the Federal Loan Home Mortgage Corporation,represents weekly 30-year fixed mortgage rates. Date Mortgage Rate (\%) October 14, 2005 6.03 October 21, 2005 6.10 October 28, 2005 6.15 November 4, 2005 6.31 November 11, 2005 6.36 November 18, 2005 6.37 November 25, 2005 6.28 December 2, 2005 6.26 December 9, 2005 6.32 December 16,2005 6.30 December 23, 2005 6.26 December 30,2005 6.22 January 6, 2006 6.21 January 13, 2005 6.15 -Refer to the table above.Use Solver to find the optimal alpha that minimizes MAD,and use exponential smoothing to forecast the next weekly mortgage rate.

A time series that is unseasonalized may exhibit a trend,a random component,and a seasonal pattern.

Use this information to answer the following questions. A hot dog stand owner has collected the following time series data on the number of hot dogs sold over the last 12 quarters. Year Quarter Demand 1 Winter 29 1 Spring 65 1 Summer 56 1 Fall 45 2 Winter 23 2 Spring 57 2 Summer 48 2 Fall 32 3 Winter 14 3 Spring 55 3 Summer 52 3 Fall 25 -Refer to the table above.Using a multiplicative decomposition model,forecast the next four quarterly sales data.

Use this information to answer the following questions. Joe Smith operates an ice cream shop and works only three days a week.The number of ice cream cones that he sells is shown as follows. Friday 100 114 110 115 112 Saturday 130 135 140 145 142 Suraday 60 65 55 50 63 -Refer to the table above.Use a linear trend line to forecast ice cream sales for the next three days.

Consider the following forecast errors.What is the Mean Absolute Deviation (MAD)? Period Error 1 -2 2 1 3 3 4 0 5 -1 6 2 7 4

Moving averages are useful in forecasting stationary time series as they tend to smooth out random variations.

Consider the following data that was fitted using a Linear Trend. Period Actual value (or) Y Period number (or) X Period 1 10 1 Period 2 11 2 Period 3 9 3 Period 4 12 4 Period 5 13 5 Period 6 12 6 Period 7 15 7 The intercept of the trend line is 8.714,and the slope is 0.75.What is the forecast for period 8?

A time series which has a significant upward or downward trend is referred to as:

A car sales manager has collected the following data on the number of cars sold per week and years of experience for 7 of his salespeople. Cars Sold/Week Years of Experience 3 1.5 7 4 5 3 10 12 8 10 6 4 4 3.5 a.Develop a regression model to predict sales based on years of experience. b.Use the estimated regression model to predict sales for a salesperson with 7 years of experience.

Use this information to answer the following questions. The following time series represent the total population of the United States,in thousands,over the last 12 years. Year Population (in 000s) 1991 253,493 1992 256,894 1993 260,255 1994 263,436 1995 266,557 1996 269,667 1997 272,912 1998 276,115 1999 279,295 2000 282,434 2001 285,545 2002 288,600 -Refer to the table above. a.Use exponential smoothing with a smoothing constant of 0.5 to forecast the population of the United States in 2003. b.Use exponential smoothing with a smoothing constant of 0.8 to forecast the population of the United States in 2003. c.Which of the two methods provides a more accurate forecast based on the MAD criterion?

If a time series exhibits a strong,linear upward trend,the value of the correlation coefficient,r,is expected to be positive and close to -1.

In using a moving average forecasting technique,as the number of averaging period,k,increases:

Use this information to answer the following questions. The following time series represent the total population of the United States,in thousands,over the last 12 years. Year Population (in 000s) 1991 253,493 1992 256,894 1993 260,255 1994 263,436 1995 266,557 1996 269,667 1997 272,912 1998 276,115 1999 279,295 2000 282,434 2001 285,545 2002 288,600 -Refer to the table above.a.What is the linear trend equation that best fits the data? b.What is the forecast of the population of the United States in 2003 using the linear trend equation? c.What is the MAPE for this method?

Use this information to answer the following questions. The following data,provided by the U.S.Bureau of Citizenship and Immigration Services,represent the number of immigrants admitted to the United States,in thousands,from 1990-2001. Year No. of Immigrants (in 000s) 1990 1536 1991 1827 1992 974 1993 904 1994 804 1995 720 1996 916 1997 798 1998 654 1999 647 2000 850 2001 1064 -Refer to the table above. a.Use a 2-period moving average to forecast the number of immigrants in 2002. b.Use a 3-period moving average to forecast the number of immigrants in 2002. c.Which averaging period provides a better historical fit based on the MAD criterion?

Use this information to answer the following questions. The following data,provided by the U.S.Bureau of Citizenship and Immigration Services,represent the number of immigrants admitted to the United States,in thousands,from 1990-2001. Year No. of Immigrants (in 000s) 1990 1536 1991 1827 1992 974 1993 904 1994 804 1995 720 1996 916 1997 798 1998 654 1999 647 2000 850 2001 1064 -Refer to the table above.Using Solver to find the optimal alpha that minimizes MAD,use exponential smoothing to forecast the number of immigrants in 2002.

In an exponential smoothing forecast,the weight associated with older data increases exponentially over time.

In general,the higher the value of the coefficient of determination R²,the better the fit of the regression model.

Use this information to answer the following questions. A hot dog stand owner has collected the following time series data on the number of hot dogs sold over the last 12 quarters. Year Quarter Demand 1 Winter 29 1 Spring 65 1 Summer 56 1 Fall 45 2 Winter 23 2 Spring 57 2 Summer 48 2 Fall 32 3 Winter 14 3 Spring 55 3 Summer 52 3 Fall 25 -Refer to the table above.Use a linear trend equation to forecast next quarterly sales.