2. Working with Multiple Variables
Response of One variable
to Change in The Other
Move together
1. Same Direction
2. Different Direction
Don’t Move Together
How much change in
one variable in
response to a unit
change in the other.
Correlation or
Association
Regression

3. Studying Multi
Variables Two Ways
Deterministic Way Probabilistic Way
Relation or Effect is Exact Relation or Effect is Non-
exact (Error Term)
Book Value
BV = P– AD = P - nD
BV = Book Value
P = Price
AD = Accumulated Depreciation
D = Depreciation
n = years
Marks Obtained
M = C + mH
M = Marks Obtained in Exam
H = Time Given to Study (Hrs)
m = increase in marks in
response to increase study by
1 hr

5. RegressionWhatisit?
Modeling of the functional relationship between a response
variable and a set of explanatory variables
The regression model tells what happens to the response
variable for specified changes in the explanatory variables.
Example
What will be the cash flows based on specified values of
interest rates, raw material costs, salary increases, and ….
A regression line, also called a line of best fit, is the line for
which the sum of the squares of the residuals is a minimum.

7. Y = b 0+𝑏 1X + e
Intercept or
Constant
Slope
Deterministic
Component
Explained by Model
Error Component
Not Explained by
Model

8. Assumption 1
The mean of each error
component is zero
Assumption 2
Each error component
follows an approximate
normal distribution
Assumption 3
Homoscedasticity
Variance of error
component is the same
for each value of X
Assumption 4
The errors are
independent of each
other
Assumptions

10. Regression Analysis
S1: Scatter Diagram
S2: Check the Assumptions
S3: Draw the Line
S4: Inference of Coefficient

11. Y
X
x y
65 175
67 133
71 185
71 163
66 126
75 198
67 153
70 163
71 159
69 151
69 155
65 70 75 80
120
130
140
150
160
170
180
190
200
Scatter Diagram

12. How the Assumptions Appear
Zero Mean of
Errors
Normally
Distributed
Errors
Independent
Errors
Constant
Variance of
Errors

13. Not Linear Linear

x
residuals
x
Y
x
Y
x
residuals
Residual Analysis for Linearity

14. Non-constant variance  Constant variance
x x
Y
x x
Y
residuals
residuals
Residual Analysis for Homoscedasticity

15. Not Independent
Independent
X
X
residuals
residuals
X
residuals

Residual Analysis for Independence

16. How to Check Regression
Assumptions

17. Estimating the Coefficient of Regression Line
What we Finally Want
How We Get it
Get all
Summations
Get these
Quantities

18. A correlation is a relationship between two variables.Correlation

19. Correlation &
Data Type
Scale Ordinal Nominal
Pearson
Correlation
Spearman
Correlation
Phi
Coefficient
Cramer’s
Coefficient
Contingency
Coefficient

20. Pearson Correlation
Data Both the variables be scale (Interval or Ratio)

21. Sums
Which are
Required
X2 Y2 XYX Y
Total

22. Values of Correlation &
Interpretation
Range -1 0 +1.5-.5
Perfectly Positive or Negative Relations
No Linear Relation
Strong Positive or Negative
Correlation
Weak Positive or
Negative Correlation

23. Value Relation
0.00 None
0.01 to 0.09 Negligible
0.10 to0.29 Weak
0.30 to 0.59 Moderate
0.60 to 0.74 Strong
0.75 to 0.99 Very Strong
1 Perfect
Values of Correlation &
Interpretation