f.
Lack of outliers in the data
Linear Regression is extremely sensitive to outliers as It affects the regression line and
eventually the forecasted values.

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5.
Two main types of Linear regression
a.
Simple Linear Regression (SLR)
In SLR, there is only one predictor (independent) variable X which changes result on
different values for response (dependent) variable, Y.
Let Y
t
denote the dependent variable, X1
t
is the independent variable for the t
th
observation. The value of Y at time t, in the sample data is determined by the linear
equation:
β0, β1 are constants and εs are independent and identically distributed normal random
variables with mean 0.
β0 and β1 are intercept and slope of the model.
Example: Regression equation between hours studied and marks scored
Marks scored = 24.16 + 0.7382 * Hours_Studied

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5.
Two main types of Linear regression
Note:
1)
The relationship is not a mathematical model relationship and hence the error term.
2)
The linearity condition is defined with respect to the regression coefficients and not with
respect to the predictor variables. Thus Y
i
= β
0
+ β
1
log
(
X
i)
+ ε
i
is a linear model but
relationship between Y and X is not linear.
3)
Regression calculates the most likely outcome based on a trend of one or more known
independent variables and the impact of changing one of the independent variables.
a.
Simple Linear Regression (SLR) - continued

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5.
Two main types of Linear regression - continued
b.
Multiple Linear Regression (MLR)
In MLR, there are more than one predictor (independent) variables X1, X2, … which
change result on different values for response (dependent) variable, Y.
Let Y
t
denote the dependent variable, X1
t
, X2
t
, …, Xk
t
are the independent variable for
the t
th
observation. The value of Y at time t, in the sample data is determined by the
linear equation:
β
0
, β
1
, … β
k
are constants and εs are independent and identically distributed normal
random variables with mean 0.
β
0
is the intercept of the model and β0, β1,β2, ...βk are regression coefficients
Example: Regression equation between hours studied, Gender and marks scored in the final examination
Marks = 19.71 + 0.72 * Hours_Studied + 10.18 * Gender.

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6.
Simple Linear Regression (SLR) Model building
Simple linear regression model helps us to understand how the value of a dependent
variable under study changes with the values of an independent variable.
Examples include:
a.
An e-commerce company such as Bigbasket, e-Bay, Amazon would like to
understand how their revenue varies with the number of customer visits to their
portal.
b.
Banks and other financial institutions would like to understand the impact of
unemployment rate on percentage of non-performing assets.
c.
Original Equipment Manufacturers would like to understand the impact of
duration of warranty on their profit.

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6.
Simple Linear Regression (SLR) Model building
Steps for building a regression model
I.
Data collection
Collect data from various sources for the identified problem. Data collection is a time consuming and

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- Regression Analysis