1. Quantitative Methods
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2. Models for Data Analysis & Interpretation: Regression Analysis
Quantitative Methods
Models for Data Analysis & Interpretation: Regression Analysis

3. Cause and Effect - Henri Bergson
The Present Contains Nothing More Than The Past, and What Is Found In The Effect Was Already In The Cause.
- Henri Bergson
(19th Century French Philosopher)
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4. Regression Model
A Statistical Model which Depicts the Influence of One Cardinal Variable (The Cause) on Another Cardinal Variable (The Effect).
These Models Have a Wide Variety of Forms and Degrees of Complexity.
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5. Regression The Step Logically Next To Correlation.
Situation: Usually, Correlation Between Two Variables Is Not Mere Benign Association. But, It Is In Fact Causation.
It Is a Cause and Effect Relationship, Where X Influences Y.
X is the Cause Variable.
Y is the Effect Variable.
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6. Some Examples Cause Effect Movie Ticket Price Multiplex Occupancy
Machine Downtime
Production
Rainfall at Night
Absenteeism Next Day
R&D Expenditure
Gross Profit ?
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7. Regression
Dictionary Says: The Act of Returning or Stepping Back to a Previous Stage.
Query: Do Quantitative Methods Force Us to Regress instead of Progress?
Or, Is It Back to the Future?
Answer: Statistics, Like Any Other Field, Adopts Crazy Names Arising from Some Important Historical Events.
Soap Opera.
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8. Story of Regression
Sir Francis Galton Studied the Heights of the Sons in Relation to the Heights of Their Fathers.
His Conclusion: Sons of Tall Fathers Were Not So Tall and Sons of Short Fathers Were Not So Short as their Fathers.
Path Breaking Finding: Human Heights Tend To Regress Back To Normalcy.
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9. Evolution of the Term ‘Regression’
Since Then (1880), Similar Studies on Nature and Extent of Influence of One or More Variables on Some Other Variable Acquired the Name ‘Regression Analysis’.
In Quantitative Methods, Regression Means a ‘Cause and Effect Relationship’.
Cause Variable = Independent Variable
Effect Variable = Dependent Variable
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10. Scatter Plot Horizontal Axis: Reasoning Scores Vertical Axis: Creativity Scores
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11. Scatter Plot Horizontal Axis: Cause Variable: Reasoning Scores Vertical Axis: Effect Variable: Creativity Scores
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12. Regression Curve Horizontal Axis: Cause Variable: Reasoning Scores Vertical Axis: Effect Variable: Creativity Scores
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13. Regression Analysis
A Quantitative Method which Tries to Estimate the Value of a Cardinal Variable (the Effect) by Studying Its Relationship with Other Cardinal Variables (the Cause).
This Relationship is Expressed by a Custom-Designed Statistical Formula Called Regression Equation.
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14. Purpose of Regression Analysis
To Establish Exact Nature of Influence of Cause Variable on Effect Variable.
To Determine the Quantum of Influence.
To Estimate an Unknown Value of Effect Variable from Value of Cause Variable.
To Forecast Future Values of Effect Variable from Info about Cause Variable
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15. Patterns of Regression Curves
Pattern: Upward Sloping Straight Line
Mathematical Model: Y = a + bX (b > 0)
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16. Estimating Regression Parameters a & b
Formula for Regression Coefficient b :
Mean of Products of Values – Product of the Two Means =
Variance of Cause Variable
Formula for Regression Constant a :
a = Mean of Effect Variable Minus b times Mean of Cause Variable
Don’t Worry. This is the Job of SPSS.
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17. Estimating Correlation Coefficient
Recall the Formula for Correlation Coeff.
Pearson’s Correlation Coefficient
Formula:
Mean of Products of Values – Product of the Two Means =
Product of the Two Standard Deviations
Spot the Similarity and the Difference.
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18. A Simple Example Empl. No. Yrs in Co. Salary (‘000) Product 1 2 25 503 30 90 5 37
185 4 7 38
266 8 40
320
Total
170
911
Arith Mean 34
Std. Dev.
2.3
5.6
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19. Regression Model Formula for Regression Coefficient b :
Mean of Products of Values – Product of the Two Means =
Variance of Cause Variable
(911 / 5) – (5 x 34) –
= = = = 2.30
2.3 x
Formula for Regression Constant a :
a = Mean of Effect Variable Minus b times Mean of Cause Variable = 34 – 2.3 x 5 = 22.5
Regression Model: Y = X
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20. Check Goodness of the Model
Empl. No.
Yrs in Co.
Salary (‘000)
Estimate 1 2 25 3 30 5 37 4 7 38 8 40
Total
170
Arith Mean 34
Std. Dev.
2.3
5.6
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21. Check Goodness of the Model
Empl. No.
Yrs in Co.
Salary (‘000)
Estimate 1 2 25
27.1 3 30
29.4 5 37
34.0 4 7 38
38.6 8 40
40.9
Total
170
Arith Mean 34
Std. Dev.
2.3
5.6
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22. Concept: Error of Estimation
Note the Difference Between the Actual Values of Effect Variable (Salary) and the Values Estimated by the Regression Model
This is the Error of Estimation
Less the Error, Better the Model. Ideally 0.
Statistical Model: Y = a + b X + e
If Correlation is Perfect (+1 or -1), e = 0.
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23. Q5.
Given below are five observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). x y a. Develop the least squares estimated regression equation. b. Estimate value of y for x=7.
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24. Exercise: Fit a Regression Model to Reasoning & Creativity Scores
Apl No,
RsnSc
CrvSc 01
15.2
11.9 11
8.1
6.8 02
9.9
13.1 12
13.0 03
7.1
8.9 13
10.9
13.9 04
17.9
17.4 14
17.2
19.1 05
5.1
6.9 15
8.2
10.1 06
10.0
8.8 16
10.8
15.9 07
7.2
14.0 17
12.0
12.1 08
17.1
15.8 18
16.0 09
9.7 19
19.2 10
9.2 20
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25. Exercise Does Your Model Look Like What I Got?:
Creativity Scores = x Reasoning Scores + e
Test the Goodness of Your Regression Model
How Bad are the Errors?
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26. Other Patterns of Regression Curves
Pattern: Downward Sloping Straight Line
Statistical Model: Y = a - bX + e (b > 0)
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27. Other Patterns of Regression Curves
Pattern: Simple Exponential
Model: Log Y = a + bX + e (b > 0)
Pattern: Negative Exponential
Model: Log (1/Y) = a + bX + e (b > 0)
Pattern: Upward Curvilinear
Model: Y = a + b Log X + e (b > 0)
Pattern: Downward Curvilinear
Pattern: Logistic or S Curve
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28. Your Role as a Manager Grasp the Situation Thoroughly. (Qualitative)
Identify Related Cardinal Variables. (DIY)
Obtain Quantitative Data on Them.
Draw Scatter Plot. Your Asstt Will Do It For You
If It Shows a Pattern, Compute Correlation Coefficient. (Use SPSS or YAWDIFY)
If It Is High (+ or -), Draw a Free Hand Curve and Identify the Pattern of Regression Curve.
Compute Regression Parameters for the Pattern and Fit Regression Model. (SPSS or YAWDIFY)
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29. A Word of Caution
Undertake Regression Analysis Only For Cardinal Variables.
Select the Variables Only If You Logically Suspect Influence of One Over the Other.
Carry Out Regression Analysis Only After Completing Correlation Analysis AND Only If The Selected Cause and Effect Variables Are Highly Correlated.
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30. Simple and Multiple Regression
Simple Regression: One Cause Variable Influences the Effect Variable.
This is What We Focused On So Far.
Regression Models Have a Wide Variety of Forms and Degrees of Complexity.
Multiple Regression: Several Cause Variables Jointly Influence Effect Variable.
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31. Multiple Regression
Multiple Regression Analysis is a Method to Analyze the Effect of Joint Influence of Many Cause Variables on Effect Variable.
Multiple Regression Model:
Y = a + b1X1 + b2X bnXn + e
Caution: Cause Variables X1, X2, , Xn Should Not Be Inter-Correlated.
Otherwise You Face Multicollinearity.
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32. Exercise: Select Cause Variables
Cause # 1 X1
Cause # 2 X2
Cause # 3 X3
Effect Y
Machine Downtime
Labour Absenteeism
Power Outage
Monthly Production
EPS ?
BASF Share Price
MRP
ManpowerRequiremt
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