Economics 173 Business Statistics Lecture 24 © Fall 2001, Professor J. Petry

2 –The moving average method does not provide smoothed values (moving average values) for the first and last set of periods Exponential Smoothing –The exponential smoothing method provides smoothed values for all the time periods observed. >the moving average method considers only the observations included in the calculation of the average value. –When smoothing the time series at time t, –exponential smoothing considers all the data available at t (yt, yt-1,…)

3 Exponentially smoothed time series S t = exponentially smoothed time series at time t. y t = time series at time t. S t-1 = exponentially smoothed time series at time t-1.  = smoothing constant, where 0 <=  <=1. S t =  y t + (1-  )S t-1

4 The process (example 20.2) Calculate the gasoline smoothed time series using exponential smoothing with  =.2. Set S 1 = y 1 S 1 = 39 S 2 = wy 2 + (1-w)S 1 S 2 = (.2)(37) + (1-.2)(39) = 38.6 S 3 = wy 3 + (1-w)S 2 S 3 = (.2)(61) + (1-.2)(38.6) = 43.1

5 The process (example 20.2) The smoothed series with  =.2 The smoothed series with  =.7 Small  provides a lot of smoothing

6 1.Using the now familiar data from Armani’s pizza, exponentially smooth the data. Week 1 Monday35 Tuesday42 Wednesday56 Thursday46 Friday67 Saturday51 Sunday39 Example

7 Project II – Human Resources Application Your team comprises Human Resources You are given a list of questions that management wants answered Criterion for hiring the most productive employees, along with a few related issues We give you the data 1 Dependent variable –Dollar sales 17 Independent Variables –Motivation of worker, enjoy customer interaction, education level, gender, work experience, age... 1,000 observations for each variable Involves dummy variables, transformations, etc

8 Project II – Human Resources Application Graph your independent variable with dependent variable as a first step to insure relationship is properly specified. You will use two regression models “Full Model”, and “Reduced Model” Selection will be based on t-tests of coefficient values, adjusted R 2 and Partial F-test (See below) Which version you use to answer which questions is generally specified in the project description—though your judgment is important General Report Guidelines still apply. Include 1 page executive summary The body of the report should be no more than 5 pages double spaced (anything beyond 5 pages will not be read). Include detailed tables, graphs, etc in a professionally formatted and presented appendix.

9 Project II – Partial F-test To determine which variables we retain and which we eliminate from a multiple regression, use: individual t-test, (beware of multicollinearity) adjusted R 2 Partial F-test –Like the F-test, used to simultaneously test whether numerous Beta coefficients equal 0. run a “full regression” with all variables included run a “reduced regression” after eliminating certain Xs use the difference in SSR b/n regressions as test statistic

10 Project II – Partial F-test