1. BUSINESS MATHEMATICS
&
STATISTICS

2. Exponential Smoothing
LECTURE 32
Time Series and
Exponential Smoothing
Part 1

3. Simple Linear Regression Equation: Example
Annual Store Square Sales Feet Rs. (000)
, ,681
, ,395
, ,653
, ,543
, ,318
, ,563
, ,760
You wish to examine the relationship between the square footage of produce stores and their annual sales. Sample data for 7 stores were obtained. Find the equation of the straight line that fits the data best

4. Scatter Diagram Example
Excel Output

5. Equation for Sample Regression Line
From Excel Printout:

6. Graph of the Sample Regression Line
Yi = Xi 

7. Interpreting the Results
Yi = Xi
The slope of means that each increase of one unit in X, we predict the average of Y to increase by an estimated units.
The model estimates that for each increase of 1 square foot in the size of the store, the expected annual sales are predicted to increase by Rs.1487

9. CHART WIZARD

10. GRAPH

17. EXAMINATION OF GRAPH TREND
General upward or downward steady behaviour of figures
Seasonal Variation
Variations which repeat themselves regularly over short term, less than a year
Random Effect
Variations due to unpredictable situations
Cyclical Variations
Alternation of upward and downward movement

18. EXTRACTING THE TREND DATA 170, 140,230,176, 152, 233, 182, 161, 242
No explanation regarding time periods
First step
Plot figures on graph
Horizontal as period 1
Vertical as period 2
Conclusion
A marked pattern that repeats itself
Well established method to extract trend with strong repeating pattern

19. DATA

21. Next Average-Afternoon
MOVING AVERAGES
First Average- Day 1
= ( )/3 = 540/3 = 180
Next Average-Morning
= ( )/3 =546/3 = 182
Next Average-Afternoon
= ( )/3 = 186
Another method
Drop 170; Add 176; = ( )/3 = 6/3 = 2
Last average + 2 = = 182
Caution
You may make a mistake

24. ANALYSING SEASONAL VARIATIONS
Find out how much each period differs from trend
Calculate Actual – trend for each period
Day 1, Afternoon
Actual = 180, Trend = 140
Actual – Trend = 140 – 180
=-40

25. BUSINESS MATHEMATICS
&
STATISTICS

26. BUSINESS MATHEMATICS
&
STATISTICS

27. EXCEL REGRESSION TOOL P-Value
If we test the hypothesis that the inercept is zero (i.e. Line passes through the origin)
We see that P-value for intercept = 0.07
Adopting 5% significant criterion
This indicates that the population intercept could well be zero