1. Dependence Technique, Regression and correlation ,
standard multiple regression
Presented By
Ms. Qurat-ul-Ain
Salman Asmat
M. Usman Ahmed
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2. Content of Presentation
o Dependence Techniques
1. Correlation
2. Regression
Simple Regression
Multiple Regression
Standard Multiple Regression
o Demonstration and Interpretation
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3. Dependence Technique
It is a statistical technique distinguished by having a
variable or a set of variables identified as dependent
variable(s) and remaining variables as independent
vaiables.The object of Dependence technique is the
prediction of dependent variables by the independent
variables. Or in simple words dependence technique is
in which variables are easily classified as dependent
and independent variables.
Examples are correlation and regression analysis
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4. Correlation
Correlation is the average relationship between two or
more variables.
It represents with r
It lies between +1 to -1
When variables are dependent on time than
correlation is applied
+1 indicates +ve correlation
-1 indicates –ve correlation
Zero correlation indicates no relationship
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5. Types of correlation.
Positive correlation
Negative correlation
Perfectly positive
Perfectly negative
Zero correlation
Linear correlation
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6. Positive correlation
When two variables moves in the same direction then
correlation between two variables are said o be positive
When the value of one variable increase ,the value of
other variable also increases at the same rate
Example:
Training and performance of employees in the
company
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7. Negative correlation
Two variables moved in the opposite direction when
value of variable increases the value of other variable
decreases
example:
The relationship between price and demand
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8. Perfect positive correlation
When there is a change in one variable, and if there is
equal proportion of change in the other variable in the
same direction then these two variables said to be in
perfectly positive correlation
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9. Types
Perfectly negative correlation:
Between two variables X and Y if the change in X
causes the same amount of change in Y in equal pro
portion but in opposite direction.
Zero correlation:
When two variables are independent and the change in
one variable has no effect in other variable
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10. Types
Linear correlation:
If the quantum change in one variable has the ratio of
change is the quantum of change in other variable is
known as linear correlation
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11. Methods of determine correlation
Following are the methods of determine the correlation
Scatter plots
Karl Pearson’s coefficient of correlation
Spearman’s rank correlation
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12. Regression Analysis
Regression analysis is the generic term for several statistical
tests for evaluating the relationship between interval level
dependent and independent variables.
When we are considering the relationship between one
dependent variable and one independent variable, we use
Simple Linear Regression.
When we are considering the relationship between one
dependent variable and more than one independent
variable, we use Multiple Regression.
SPSS uses the same procedure for both Simple Linear
Regression and Multiple Regression, which adds some
complications to our interpretation.
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13. Purpose of Simple Linear
Regression
The purpose of simple linear regression analysis is to
answer three questions that have been identified as
requirements for understanding the relationship between
an independent and a dependent variable:
Is there a relationship between the two variables?
How strong is the relationship (e.g. trivial, weak, or strong;
how much does it reduce error)?
What is the direction of the relationship (high scores are
predictive of high or low scores)?
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14. Example of simple linear
Regression
There is a relationship between undergraduate GPA’s
and graduate GPA’s.
GRE scores are a useful predictor of graduate GPA’s.
For social work students, the relationship between
GPA and future income enables us to predict future
earnings based on academic performance.
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15. The Regression Equation
The regression equation is the algebraic formula for the
regression line, which states the mathematical relationship
between the independent and the dependent variable.
We can use the regression line to estimate the value of the
dependent variable for any value of the independent
variable.
The stronger the relationship between the independent and
dependent variables, the closer these estimates will come to
the actual score that each case had on the dependent
variable.
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16. Simple Linear Regression:
Hypotheses
The hypothesis tested in simple linear regression is
based on the slope or angle of the regression line.
Hypotheses:
Null: the slope of the regression line as measured by the
b coefficient = 0, i.e. there is no relationship
Research: the slope of the regression line as measured by
the b coefficient ≠ 0, i.e. there is a relationship
Decision:
Reject null hypothesis if pSPSS ≤ alpha
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17. Standard Regression Equation
The standard form for the regression equation or
formula is:
Y = a + bX
where
Y is the estimated score for the dependent variable
X is the score for the independent variable
b is the slope of the regression line, or the multiplier of
X
a is the intercept, or the point on the vertical axis where
the regression line crosses the vertical y-axis
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18. Purpose of Multiple Regression
The purpose of multiple regression is to analyze the
relationship between metric independent variables
and a metric dependent variable.
If there is a relationship, using the information in the
independent variables will improve our accuracy in
predicting values for the dependent variable.
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19. interpretation
The last column shows the goodness of fit of the
model. The lower this number, the better the fit.
Typically, if “Sig” is greater than 0.05, we conclude
that our model could not fit the data.
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20. R-square:
Measures the proportion of the variation in the
dependent variable (wage) that was explained by
variations in the independent variables. In this
example, the "R-Square"' tells us that 51% of the
variation (and not the variance) was explained.
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21. Adjusted R-square:
Measures the proportion of the variance in the dependent
variable (wage) that was explained by variations in the
independent variables. In this example, the “Adjusted R
Square” shows that 50.9% of the variance was explained.
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26. Types of Multiple Regression
Standard multiple regression
Hierarchical multiple regression
Stepwise multiple regression
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27. Standard Multiple Regression
• Standard multiple regression is used to evaluate the
relationships between a set of independent variables and a
dependent variable.
• In standard multiple regression, all of the independent
variables are entered into the regression equation at the
same time
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