1. STATISTICS 13.0 Linear Time Series Trend “Time Series ”- Time Series Forecasting Method

2. Time Series Characteristics –Time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals –The oldest mode of forecasting, most widely used for estimating demand in aviation industry –Time series analysis comprises methods for analysing time series data in order to extract meaningful statistics and other characteristics of the data. 13.0 Linear Time Series Trend

3. Independent Variables vs Time The number of average goals Wayne Rooney score annually Year ( t ) Goals ( Y t ) 200121.6 200222.9 200325.5 200421.9 200523.9 200627.5 200731.5 200829.7 200928.6 201031.4 13.0 Linear Time Series Trend

4. Independent Variables vs Time –The year for the data is considered time ( t ), the goals scored is considered the independent variable ( Y t ) at that particular time –From the coordination of the data plotted in time series, we can determine a dependent variable (T t ), which is the trend value of the time series in period t –Unlike causal models, there is hardly statistical correlation since it does not necessarily reflect ( t ) cause ( Y t ) 13.0 Linear Time Series Trend

5. Time Series Trend 1)The technique of simple liner trend enables us to describe an equation of straight line that best fits a series of ordered pairs ( t,Y t ) 2) The convention is to place the t variable on the horizontal axis and the Y t variable on the vertical axis. 3) The equation for a straight line, known as a linear equation, take from: T t = b o + b t t 13.0 Linear Time Series Trend b o = intercept of the trend line T t = trend value of the time series in period t b o = intercept of the trend line b t = slope of the trend line t = time

6. Time Series Trend 4)The least squares method finds the linear equation to calculate b o, the intercept of the trend line and b t, the slope: b t = ∑ t Y t – (∑ t ∑Y t )/n b o = Y t – b t t ∑ t ² -(∑ t )²/n t = the average value of t, ∑ t /n Y t = the average value of the time series, ∑Y t /n 13.0 Linear Time Series Trend n = number of periods

7. The number of average goals Wayne Rooney score annually Year ( t ) Goals ( Y t ) 200121.6 200222.9 200325.5 200421.9 200523.9 200627.5 200731.5 200829.7 200928.6 201031.4 Exercise a)Graph this time series for the number of goals that Wayne Rooney score b) Develop a linear trend equation for this time series c) Forecast the number of goals that he will score on 2015