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# Lesson 5

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### Lesson 5

1. 1. Hanze University of Applied Science GroningenNing Ding, PhDLecturer of International BusinessSchool (IBS)n.ding@pl.hanze.nl
2. 2. What we are going to learn? • Review • Chapter 16: – Define the components of a time series – Compute a moving average – Determine a linear trend equation
3. 3. Review Ŷ = a + bX Standard Error Y Axis: Dependent Variable• Review Standard 7 Error r2 = 1 r = -1• Chapter 16: Standard Error = 0–Define thecomponents of a 6time series r2 = 0.24 r = -0.49–Compute a 5 Standard Error = 2.5moving average–Determine a 4linear trendequation Individual values are 3. more scattered from the regression line. 2 1 1 2 3 4 5 6 7 X Axis: Independent Variable
4. 4. Review Perfect •Coefficient of determination: r2=+1• Review •Coefficient of correlation: r=+1 Correlation •Standard Error: SE=0• Chapter 16:–Define the 1994-1997 Motorcycle Sales in Canada Salescomponents of a 1000time series 900–Compute a 800moving average 700–Determine a 600linear trendequation 500 Sales 400 300 200 100 0 0 50,000 100,000 150,000 200,000 1994-1997 GDP in Canada (In millions of CAD)
5. 5. Review Perfect • r2=+1 100% of Sales variations are explained by• Review GDP variations. Correlation • r=+1 There is a positive and perfect correlation• Chapter 16: between motorcycle sales and GDP.–Define the 1994-1997 Motorcycle Sales in Canada • SE=0 Salescomponents of a 1000time series 900–Compute a 800moving average 700–Determine a 600linear trendequation 500 Sales 400 300 200 100 0 0 50,000 100,000 150,000 200,000 1994-1997 GDP in Canada (In millions of CAD)
6. 6. Review Perfect • r2=+1 100% of Sales variations are explained by• Review GDP variations. Correlation • r= -1 There is a negative and perfect correlation• Chapter 16: between motorcycle sales and GDP.–Define the • SE=0components of a 1994-1997 Motorcycle Sales in Canadatime series Sales 1000–Compute a 900moving average 800–Determine a 700linear trend 600equation 500 Sales 400 300 200 100 0 0 50,000 100,000 150,000 200,000 1994-1997 GDP in Canada (In millions of CAD)
7. 7. Review Strong • r2=+0.88 88% of Sales variations are explained by• Review GDP variations. Correlation There isrelationshipand strong correlation • r= -0.94 The a negative gets weaker.• Chapter 16: between motorcycle sales and GDP.–Define the • SE=35.92 The data scattering increases.components of a 1994-1997 Motorcycle Sales in Canadatime series Sales 1000–Compute a 900moving average 800–Determine a 700linear trend 600equation 500 Sales 400 300 200 100 0 0 50,000 100,000 150,000 200,000 1994-1997 GDP in Canada (In millions of CAD)
8. 8. Review Moderate • r2=+0.34 34% of Sales variations are explained• Review by GDP variations. Correlation • r= -0.59 There relationship gets weaker. The is a negative and moderate• Chapter 16: correlation between sales and GDP.–Define thecomponents of a • SE=35.92 The data scattering increases. 1994-1997 Motorcycle Sales in Canadatime series–Compute a Salesmoving average 1200–Determine a 1000linear trendequation 800 600 Sales 400 200 0 0 50,000 100,000 150,000 200,000 1994-1997 GDP in Canada (In millions of CAD)
9. 9. Review gender, income, eye colour, distance• Review a. Qualitative b. Quantitative• Chapter 16:–Define thecomponents of atime series age in years temperature IQ–Compute amoving average a. Nominal b. Ordinal c. Interval d. Ratio–Determine alinear trendequation Discrete counting or Continuous measuring
10. 10. Review Qualitative Data• Review• Chapter 16:–Define thecomponents of atime series–Compute amoving average–Determine alinear trendequation Quantitative Data
11. 11. Review• Review Ungrouped Data Grouped Data• Chapter 16: Classes f–Define the 10 up to 20 2components of atime series 20 up to 30 1 1 2 2 3 4–Compute a 30 up to 40 4moving average–Determine a 10-<20 2 2 *15=30linear trendequation Mean (1+2+2+3+4)/5 20 -<30 1 1 *25=25 30-<40 4 4 *35=140 195 Central Tendency Mode 7 =24.86 10-<20 2 L=(N+1)/2 Median 20-<30 3 (7+1)/2=4 30-<40 7 30 32.5 40 3 4 5 6 7
12. 12. Review a. Positive skewness b. Negative skewness c. Symmetric distribution• The distribution Review the right is skewed to __________ because the mean is __________the median. larger than• Chapter 16:–Define thecomponents of atime series–Compute amoving average–Determine alinear trendequation Interquartile Range Mean =23.06 P42 Example Ch2
13. 13. Review r = 0.9 r = -0.9 r=0 r = 0.6 r = -0.6• Review• Chapter 16: Strong & Positive Moderate & Positive–Define the correlation correlationcomponents of atime series–Compute amoving average–Determine alinear trendequation No correlation Moderate & Negative Strong & Negative correlation correlation Ŷ = a + bX
14. 14. Review• Review• Chapter 16:–Define thecomponents of atime series–Compute amoving average–Determine a X The graph is positive.linear trendequation X There is a strong determination. X It is a srong positive correlation. X r =0.8619 so 86.19% of the variation in Y is explained by the variation in X. X r2=1.05 r = √ 1.05 = 1.025 = \$1.025 X The correlation goes down.
15. 15. Chapter 16 Time Series• Review Time series: a collection of data recorded over a period of time• Chapter 16: (weekly, monthly, quarterly), an analysis of history, that can be used by–Define the management to make current decisions and plans based on long-termcomponents of a forecasting.time series–Compute amoving average–Determine alinear trendequation
16. 16. Chapter 16 Time Series• Review• Chapter 16: – S Secular Trend–Define thecomponents of a – Lineartime series–Compute a – Nonlinearmoving average – C Cyclical variation–Determine alinear trend – Rises and Falls over periods longer than one yearequation S Seasonal variation – – Patterns of change within a year, typically repeating themselves I Irregular variation
17. 17. Chapter 16 Time Series• Review S Secular Trend:• Chapter 16: The smooth long-term direction of a time series.–Define thecomponents of atime series–Compute amoving average–Determine alinear trendequation
18. 18. Chapter 16 Time Series• Review C Cyclical Variation: The rise and fall of a time series over periods longer• Chapter 16:–Define the than one year.components of atime series–Compute amoving average–Determine alinear trendequation
19. 19. Chapter 16 Time Series• Review S Seasonal Variation: Patterns of change in a time series within a year. These• Chapter 16:–Define the patterns tend to repeat themselves each year.components of atime series–Compute amoving average–Determine alinear trendequation
20. 20. Chapter 16 Time Series• Review I Irregular Variation: • Episodic – unpredictable but identifiable• Chapter 16: • Residual – also called chance fluctuation and–Define thecomponents of a unidentifiabletime series–Compute amoving average–Determine alinear trendequation
21. 21. Chapter 16 Time Series• Review Moving Average: •Useful in smoothing time series to see its trend• Chapter 16:–Define the •Basic method used in measuring seasonal fluctuationcomponents of atime series–Compute amoving average–Determine alinear trendequation
22. 22. Chapter Seven-Year Moving Series Average 16 Time Total Moving 1+2+3+4+5+4+3=22 / 7 = 3.143 2+3+4+5+4+3+2=23 / 7 = 3.286 3+4+5+4+3+2+3=24 / 7 = 3.429
23. 23. Chapter 16 Time Series Moving Average:• Review• Chapter 16:–Define thecomponents of atime series–Compute amoving average–Determine alinear trendequation
24. 24. Chapter 16 Time Series• Review• Chapter 16:–Define thecomponents of atime series–Compute amoving average–Determine alinear trendequation
25. 25. Chapter 16 Time Series• Review Linear Trend The long term trend of many business series often• Chapter 16:–Define the approximates a straight linecomponents of atime series–Compute amoving average–Determine alinear trendequation
26. 26. Chapter 16 Time Series• Review Linear Trend• Chapter 16: •Use the least squares method in Simple Linear–Define thecomponents of a Regression (Chapter 12) to find the best lineartime series relationship between 2 variables–Compute amoving average–Determine alinear trend Ŷ = a + bX Ŷ = a + btequation •Code time (t) and use it as the independent variable •E.g. let t be 1 for the first year, 2 for the second, and so on (if data are annual)
27. 27. Chapter 16 Time Series •Code time (t) and use it as the independent variable• Review •E.g. let t be 1 for the first year, 2 for the second, and• Chapter 16: so on (if data are annual)–Define the xy - nx ycomponents of a Ŷ = a + bt b= a = Y - bX -nx 2 2time series x–Compute a Example:moving average–Determine a The sales of Jensen Foods, a small grocery chain locatedlinear trendequation in southwest Texas, since 2005 are: Year Sales (\$ mil.) Year t Sales (\$ mil.) 2005 7 2005 -2 7 2006 10 2006 -1 10 2007 9 2007 0 9 2008 11 2008 1 11 2009 13 2009 2 13
28. 28. Chapter 16 Time Series Ŷ = a + bt xy a=Y b= 2 Step 1 x Step 2 Sales Year t (\$ mil.) 2005 -2 7 2006 -1 10 2007 0 9 2008 1 11 2009 2 13 Step 3 13 - 0 Step 4 a = 10 = 6.1 Step 5b= = 1.3 10 - 0 Ŷ = 10 + 1.3t
29. 29. Chapter 16 Time Series Ŷ = 10 + 1.3t• Review ? 2011 ? Ŷ = 10 + 1.3*4 = \$ 15.2 millions• Chapter 16: Example:–Define thecomponents of a The sales of Jensen Foods, a small grocery chain located in southwesttime series Texas, since 2005 are:–Compute amoving average Sales–Determine alinear trend Year t (\$ mil.)equation 2005 -2 7 2006 -1 10 2007 0 9 2008 1 11 2009 2 13
30. 30. Exercise • The amounts spent in vending machines in the United States,• Review in billions of dollars, for the years 1999 through 2005 are given• Chapter 16: below. Determine the least-squares trend equation and–Define the estimate vending sales for 2007.components of atime series a. 29.4 b. 31.3 c. 31.8 d. 32.5 e. 42.6–Compute amoving average–Determine alinear trendequation P152 N6 Ch16
31. 31. Ŷ = a + bt Exercise xy a = Y b= 2 x Step• Review 1 Code the year a. 29.4 b. 31.3 c. 31.8 d. 32.5 e. 42.6• Chapter 16: Step 2 Calculate X*Y, X2–Define thecomponents of atime series–Compute amoving average–Determine alinear trendequation Step 3 What is the b? Step 5 Formulate the least square equation Step 4 What is the a? Ŷ = ? + ?*t P152 N6 Ch16
32. 32. Exercise Ŷ = a + bt• Review 48.3 - 0 Ŷ = 22.67 + 1.73t b= = 1.73 a = 22.67• Chapter 16: 28 - 0–Define thecomponents of atime series–Compute amoving average–Determine alinear trendequation xyb= 2 xa=Y P152 N6 Ch16
33. 33. Exercise a. 29.4 b. 31.3 c. 31.8 d. 32.5 e. 42.6• Review• Chapter 16:–Define thecomponents of atime series–Compute amoving average–Determine alinear trendequation 2006 4 Ŷ 2007 5 Ŷ = 22.67 + 1.73t Ŷ = 22.67 + 1.73*5 = \$31.32 billions P152 N6 Ch16
34. 34. Review• Review •Review• Chapter 16:–Define thecomponents of atime series–Compute a •Chapter 16:moving average–Determine a –Define the components of a time serieslinear trendequation –Compute a moving average –Determine a linear trend equation