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Working with Multiple Variables
Response of One variable
to Change in The Other
Move together
1. Same Direction
2. Differe...
Studying Multi
Variables Two Ways
Deterministic Way Probabilistic Way
Relation or Effect is Exact Relation or Effect is No...
RegressionWhatisit?
Modeling of the functional relationship between a response
variable and a set of explanatory variables...
Y = b 0+𝑏 1X + e
Intercept or
Constant
Slope
Deterministic
Component
Explained by Model
Error Component
Not Explained by
M...
Assumption 1
The mean of each error
component is zero
Assumption 2
Each error component
follows an approximate
normal dist...
Regression Analysis
S1: Scatter Diagram
S2: Check the Assumptions
S3: Draw the Line
S4: Inference of Coefficient
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
1...
How the Assumptions Appear
Zero Mean of
Errors
Normally
Distributed
Errors
Independent
Errors
Constant
Variance of
Errors
Not Linear Linear

x
residuals
x
Y
x
Y
x
residuals
Residual Analysis for Linearity
Non-constant variance  Constant variance
x x
Y
x x
Y
residuals
residuals
Residual Analysis for Homoscedasticity
Not Independent
Independent
X
X
residuals
residuals
X
residuals

Residual Analysis for Independence
How to Check Regression
Assumptions
Estimating the Coefficient of Regression Line
What we Finally Want
How We Get it
Get all
Summations
Get these
Quantities
A correlation is a relationship between two variables.Correlation
Correlation &
Data Type
Scale Ordinal Nominal
Pearson
Correlation
Spearman
Correlation
Phi
Coefficient
Cramer’s
Coefficien...
Pearson Correlation
Data Both the variables be scale (Interval or Ratio)
Sums
Which are
Required
X2 Y2 XYX Y
Total
Values of Correlation &
Interpretation
Range -1 0 +1.5-.5
Perfectly Positive or Negative Relations
No Linear Relation
Stro...
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 V...
Regression & correlation
Regression & correlation
Regression & correlation
Regression & correlation
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Regression & correlation

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Regression & correlation

  1. 1. 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
  2. 2. 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
  3. 3. 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.
  4. 4. Y = b 0+𝑏 1X + e Intercept or Constant Slope Deterministic Component Explained by Model Error Component Not Explained by Model
  5. 5. 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
  6. 6. Regression Analysis S1: Scatter Diagram S2: Check the Assumptions S3: Draw the Line S4: Inference of Coefficient
  7. 7. 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
  8. 8. How the Assumptions Appear Zero Mean of Errors Normally Distributed Errors Independent Errors Constant Variance of Errors
  9. 9. Not Linear Linear  x residuals x Y x Y x residuals Residual Analysis for Linearity
  10. 10. Non-constant variance  Constant variance x x Y x x Y residuals residuals Residual Analysis for Homoscedasticity
  11. 11. Not Independent Independent X X residuals residuals X residuals  Residual Analysis for Independence
  12. 12. How to Check Regression Assumptions
  13. 13. Estimating the Coefficient of Regression Line What we Finally Want How We Get it Get all Summations Get these Quantities
  14. 14. A correlation is a relationship between two variables.Correlation
  15. 15. Correlation & Data Type Scale Ordinal Nominal Pearson Correlation Spearman Correlation Phi Coefficient Cramer’s Coefficient Contingency Coefficient
  16. 16. Pearson Correlation Data Both the variables be scale (Interval or Ratio)
  17. 17. Sums Which are Required X2 Y2 XYX Y Total
  18. 18. 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
  19. 19. 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

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