Lesson05

IBS Statistics
Year 1
Dr. Ning DING
n.ding@pl.hanze.nl
I.007

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

Chapter 12: Sim Reg & Corr
Exercise
Ŷ= -1.8182 + 0.1329X
Sample Exam P.4

r2
Review
Chapter 16:
98.87%
SD
increase
Ŷ= -1.8182 + 0.1329X
a

Review Chapter 1
Nominal: gender
Ordinal:ranking
Interval:temperature, IQ
Ratio:age in years
Qualitative:
gender, eye color,
Quantitative:
income, distance
Review
Chapter 16:
true zero
Discrete counting or Continuous measuring

Review Chapter 2
Pie Chart
Bar Chart
Cumulative Frequency
Distribution
Histogram
Polygon
Qualitative Data
Review
Chapter 16:
Quantitative Data

Review Chapter 3
195
7
=24.86
40
32.5
30
3
7
4
5
6
Ungrouped Data
Grouped Data
Review
Chapter 16:
Classes f
10 up to 20 2
20 up to 30 1
30 up to 40 4
1 2 2 3 4
2 *15=30
1 *25=25
4 *35=140
10-<20 2
20 -<30 1
30-<40 4
Mean
(1+2+2+3+4)/5
Mode
Central Tendency
10-<20 2
20-<30 3
30-<40 7
L=(N+1)/2
(7+1)/2=4
Median

Review Chapter 3
195
7
=24.86
Grouped Data
Ungrouped Data
Review
Chapter 16:
10 up to 20 2
20 up to 30 1
30 up to 40 4
1 2 2 3 4
Range
4-1=3
Variance
Dispersion
Standard Deviation

Review Chapter 4
Interquartile Range
The distribution is skewed to __________
because the mean is __________the median.
the right
Review
Chapter 16:
larger than
P42 Example Ch2
Mean =23.06

ReviewChapter 12
r = 0.9
r = -0.9
r = 0.6
r = -0.6
r = 0
Review
Chapter 16:
Strong & Positive
correlation
Moderate & Positive
correlation
No
correlation
Moderate & Negative
correlation
Strong & Negative
correlation
Ŷ = a + bX

ReviewChapter 12
Standard Error
Ŷ = a + bX
Review
Chapter 16:
Y Axis: Dependent Variable
Standard Error
r2 = 1 r = -1
Standard Error = 0
7
6
5
4
3.
2
1
r2 = 0.24 r = -0.49
Standard Error = 2.5
Individual values are more scattered from the regression line.
X Axis:
Independent Variable
1 2 3 4 5 6 7

ReviewChapter 12
Least Square Regression Equation
Ŷ = a + bX
Review
Chapter 16:

Ŷ= -1.8182 + 0.1329X
Review
Chapter 16:
Sample Exam P.4

ReviewChapter 12
Review
Chapter 16:
The graph is positive.
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

Chapter 16:
Time Series & Forecasting
Review
Chapter 16:

Components of a Time Series
Time series:
a collection of data recorded over a period of time (weekly, monthly, quarterly), an analysis of history, that can be used by management to make current decisions and plans based on long-term forecasting.
Review
Chapter 16:
S
Secular Trend
Linear
Nonlinear
Cyclical variation
Rises and Falls over periods longer than one year
Seasonal variation
Patterns of change within a year, typically repeating themselves
Residual variation
C
S
R

Components of a Time Series
Secular Trend:
The smooth long-term direction of a time series.
Review
Chapter 16:

Cyclical Variation:
The rise and fall of a time series over periods longer than one year.
Review
Chapter 16:

Seasonal Variation:
Patterns of change in a time series within a year. These patterns tend to repeat themselves each year.
Review
Chapter 16:

Irregular Variation:
Episodic – unpredictable but identifiable
Residual – also called chance fluctuation and unidentifiable
Review
Chapter 16:

Moving Average:
Useful in smoothing time series to see its trend
Basic method used in measuring seasonal fluctuation
Review
Chapter 16:

Seven-Year Moving Total
Moving Average
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
Review
Chapter 16:

Moving Average:
Review
Chapter 16:

Review
Chapter 16:

Linear Trend
The long term trend of many business series often approximates a straight line
Review
Chapter 16:

Linear Trend
Use the least squares method in Simple Linear Regression (Chapter 12) to find the best linear relationship between 2 variables
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)
Review
Chapter 16:
Ŷ = a + bX
Ŷ = a + bt

Linear Trend
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)
Review
Chapter 16:
Ŷ = a + bt
Example:
The sales of Jensen Foods, a small grocery chain located in southwest Texas, since 2005 are:
a = Y - bX

Linear Trend
Ŷ = a + bt
Step 1
Step 2
Review
Chapter 16:
a = Y - bX
Step 5
= 1.3
Step 3
Ŷ = 6.1 + 1.3t
a = 10 -1.3*3 = 6.1
Step 4

Linear Trend
Ŷ = 6.1 + 1.3*7 = 15.2
? 2011 ?
$ millions
Review
Chapter 16:
Ŷ = 6.1 + 1.3t
Example:
The sales of Jensen Foods, a small grocery chain located in southwest Texas, since 2005 are:

Exercise
The amounts spent in vending machines in the United States, in billions of dollars, for the years 1999 through 2005 are given below. Determine the least-squares trend equation and estimate vending sales for 2007.
Review
Chapter 16:
P152 N6 Ch16

Exercise
= 1.73
Ŷ = a + bt
a = 22.67 -1.73*4 = 15.75
Review
Chapter 16:
a = Y - bX
P152 N6 Ch16

Exercise
Review
Chapter 16:
8 Ŷ
2007 9
= 1.73
a = 22.67 -1.73*4 = 15.75
Ŷ = 15.75 + 1.73*9 = $31.32 billions
Ŷ = 15.75 + 1.73t
P152 N6 Ch16

Hint
Ŷ = a + bt
Step 1
Code the year
Step 2
Calculate X*Y, X2
a = Y - bX
Step 3
Step 5
Formulate the least square equation
What is the b?
Ŷ = ? + ?*t
Step 4
What is the a?
P152 N6 Ch16

What we have learnt?
Review
Chapter 16:

Lesson05

by Ning Ding on Sep 14, 2011

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