Welcome to MM305 Business Statistics with Quantitative Analysis

1. Welcome to MM305Business Statistics with Quantitative Analysis Regression Analysis and Forecasting Unit 6 Seminar Janet Kaplan JKaplan3@kaplan.edu

2. Forecasting • During the course of operation, businesses accumulate all kinds of historical data regarding sales, profit, clients, employees, pricing, competition, etc. • A number of quantitative methods are used to process those data and produce forecasts that help improve business decisions. • Of those methods, regression analysis is among the most frequently utilized, it can be used to: • examine the relationship between variables, and • predict the value of one variable based on the values of other variables.

3. Independent variable Independent variable Dependent variable = Regression Analysis • The variable to be predicted is called the dependent variable, and sometimes response variable. • The value of the dependent variable depends on the value of one or more variables called independent variables, and sometimes explanatory or predictorvariables. +

4. Simple Linear Regression • A simple linearregression modelattempts to show the relationship between one dependent variable, Y, and one independent variable, X, using a linear equation like this one, • where

5. Simple Linear Regression–Applications • Sales Forecasts • An analysis of monthly sales could show a steady upward trend in sales that the company could use to forecast sales in future months. • Product Pricing • An analysis of quantity of a product sold at various price levels may produce a line depicting price sensitivity, which could help guide future pricing decisions. • Risk Assessment • A health insurance company might conduct a linear regression plotting number of claims per customer against age. The results might guide important risk-related business decisions.

6. Multiple Linear Regression • A multiple linear regression model attempts to show the relationship between one dependent variable, Y, and various independent variables, X1, X2, …, Xk using a linear equation like this one: • where

7. Multiple Linear Regression–Applications • Employee Compensation • The dependent variable might be salary, while independent variables might include factors such as: scope of responsibility, work experience, seniority, education, etc. • Real Estate Pricing • The dependent variable might be the price of the house. Independent variables might include factors such as: size, neighborhood, number of bedrooms, number of baths, age, etc.

8. Regression Analysis Calculations • For step-by-step explanations of how to use PHStat and Data Analysis to perform the calculations associated with regression analysis, I recommend to watch the video Simple and Multiple Regression, available in the Unit 6 Live Binder.

9. Forecasting–Introduction • Businesses are always trying to reduce uncertainty and make good estimates of what will happen in the future. This is the main purpose of forecasting. • Some firms use subjective methods, based on intuition, experience, etc. • There are also quantitative techniques, e.g.: • Moving averages • Exponential smoothing • Trend projections • Least squares regression analysis

10. Eight Steps Forecasting Method • Eight steps to forecasting: • 1. Determine the use of the forecast. • 2. Select the items or quantities to be forecasted. • 3. Determine the time horizon of the forecast. • 4. Select the forecasting model or models. • 5. Gather the data needed to make the forecast. • 6. Validate the forecasting model. • 7. Make the forecast. • 8. Implement the results.

11. Forecasting–Introduction • These steps are a systematic way of designing, and implementing a forecasting system. • When used regularly over time, data is collected routinely and calculations performed automatically. • There is seldom one clearly superior forecasting technique. • Different organizations may use different techniques. • Whatever tool works best for a firm is the one that should be used.

12. Qualitative Models Time-Series Methods Causal Methods Regression Analysis Delphi Methods Moving Average Jury of Executive Opinion Multiple Regression Exponential Smoothing Trend Projections Sales Force Composite Decomposition Consumer Market Survey Forecasting Techniques Forecasting Techniques

13. Qualitative Models • Qualitative models • incorporate judgmental or subjective factors, e.g., opinions by experts, individual experiences and judgments, etc. • are especially useful when subjective factors are expected to be very important or when accurate quantitative data are difficult to obtain. • are frequently utilized in long-term forecasting.

14. Qualitative Models • Delphi Method – This is an iterative group process where (possibly geographically dispersed) respondents provide input to decision makers. • Jury of Executive Opinion – This method collects opinions of a small group of high-level managers, possibly using statistical models for analysis. • Sales Force Composite – With this method, individual salespersons estimate the sales in their region and the data is compiled at a district or national level. • Consumer Market Survey – Input is solicited from customers or potential customers regarding their purchasing plans.

15. Time-Series Models • A time-series model attempts to predict the future based on the past. • Commonly used time-series models are: • Moving average. • Exponential smoothing. • Trend projections. • Decomposition. • Regression analysis is used in trend projections and one type of decomposition model.

16. Causal Models • Causal models use variables or factors that might influence the quantity being forecasted. • Regression analysis is the most common technique used in causal modeling. • The objective is to build a model with the best statistical relationship between the variable being forecasted and the independent variables.

17. Measures of Forecast Accuracy • To assess how well a model works and to compare models we compare forecast values with actual values. • Forecast error = Actual value – Forecast value • One measure of forecast accuracy is the mean absolute deviation (MAD): • Another measure of forecast accuracy is the mean absolute percent error (MAPE):

18. Measures of Forecast Accuracy

19. Time-Series Forecasting Models • A time seriesis a sequence of events evenly spaced over time. • Time-series forecasts attempt to predict future variable based solely on past values of it. Other factors are ignored.

20. Components of a Time-Series • A time series typically has four components: • 1. Trend (T) − gradual upward or downward movement of the data over time. • 2. Seasonality (S) − pattern of fluctuations above or below the trend line that repeats at regular intervals. • 3. Cycles (C) − patterns in annual data that occur every several years. • 4. Random variations (R) − “blips” in the data caused by chance or unusual situations, that follow no discernible pattern.

21. Seasonal Peaks Demand for Product or Service | | | | Year Year Year Year 1 2 3 4 Time Decomposition of a Time-Series • Product Demand Charted over 4 Years, with Trend and Seasonality Indicated Trend Component Actual Demand Line Average Demand over 4 Years Figure 5.3

22. Time-Series Forecasting Techniques • We will use the following methods: • Moving Averages (MA) • Weighted Moving Averages (WMA) • Exponential Smoothing (ES)

23. Time-Series Forecasting Calculations • For step-by-step explanations of how to use Excel QM to perform the calculations associated with time-series forecasting I recommend to watch the video Time Series Forecast, available in the Unit 6 Live Binder.

24. Moving Averages • Moving averages (MA) is a series of arithmetic means • Used if there is little or no trend • Used oftenfor “smoothing” • Provides overall impression of data over time • Equation:

25. 3-Year Moving Averages Using Excel QM–Example

26. Weighted Moving Averages • Weighted moving averages (WMA) emphasize more recent periods. They are often used when a trend or other pattern emerge. • Equation:

27. Weighted Moving Averages Using Excel QM–Example

28. Exponential Smoothing • Exponential smoothing (ES)is a type of moving average. • It requires little record keeping. • Weights decline exponentially • Most recent data is weighted most • It uses a smoothing constant,α,ranging from 0 to 1. • Equation:

29. Selecting the Smoothing Constant [] • Selecting an appropriate value for  is key to obtaining a good forecast. • The usual approach is to develop several trial forecasts with different values of  and then select the value that results in the lowest mean absolute deviation, MAD.

30. Exponential Smoothing Using Excel QM–Example • Port of Baltimore • Program 5.2B

31. Comparison of MA and ES • Similarities: • Both are appropriate for stationary series • Both depend on a single parameter • Both lag behind a trend • Differences: • ES carries all past history (forever!) • MA eliminates “bad” data after N periods. • ES only requires last forecast and last observation (data point) to continue. • MA requires all N past data points to compute new forecast estimate.

32. Moving Average and Exponential Smoothing

33. Moving Average and Exponential Smoothing

34. Trend Projection • A trend projection fits a trend line to a series of historical data points • The line is projected into the future for medium- to long-range forecasts • Several trend equations can be developed based on exponential or quadratic models • The simplest is a model developed using linear regression analysis

35. Trend Projection • The mathematical formula is • where

36. Midwestern Manufacturing Trend Line • Excel Input Screen Program 5.4A

37. Midwestern Manufacturing Trend Line • Excel Output Program 5.4B

38. Excel QM—Regression/Trend Analysis

39. Midwestern Manufacturing Company Example • The forecast equation is • To project demand for 2008, we use X = 8 • (sales in 2008) = 56.71 + 10.54(8) = 141.03, or 141 generators • Likewise for X = 9 • (sales in 2009) = 56.71 + 10.54(9) = 151.57, or 152 generators

40. Unit 6 Graded Assignments • By Tuesday at midnight you should have completed the following graded assignments: • Discussion • Seminar • Quiz