Simple Linear Regression
Terms
Independent Variables
Dependent Variables
Simple Linear Regression Model
Simple Linear Regression Equation
Estimated Simple Linear Regression Equation
Slope for the Estimated Regression Equation
Yintercept for Estimated Regression Equation
Sum of Squares Due to Error
Total Sum of Squares
Relationship among SST, SSR, SSE
Coefficient of Determination
Correlation Coefficient
Homoscadacity
Heteroscadacity
Simple linear regression model
Simple linear regression focuses on two variables, an independent and a dependent, and their relationship
is estimated by a straight line. The equation for a simple linear regression straight line takes the form of:
y
i
= α + βx
i
+ є
Alternatively it can be written as:
y
i
= β
0
+ β
1
x
i
+ є
Where y is the dependent variable,
α
or β
0
is the yintercept, β or β
1
is the
slope, x
is the independent variable, and
∈
is the error term
For model to be correct the population of error terms have to have a
mean of zero, be independent and have a constant standard deviation
throughout the range of the x values. The error
terms also have to be
normally distributed.
One additional necessary assumption is that there
exist a linear relationship between x and y.
As stated, with simple linear regression, the dependent variable is a linear function of the independent
variable. When the ‘ x ‘ term changes by 1 the ‘ y ‘ term changes by beta, β.
There are several assumptions made about the error term є.
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It is a random variable with an expected mean of zero,
E
(є) = 0.
•
The variance of the error term, σ
2
, is the same for all values of ‘ x ‘. This is called the assumption
of homoscedasticity. Hetero scadasticity is when the error terms are not equal spread around the
regression line. The error terms may be increasing or decreasing , but there spread is not constant.
•
It is randomly distributed following a normal distribution
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 Summer '10
 chandrasekhar
 Statistics, YIntercept, Coefficient Of Determination, Linear Regression, Regression Analysis, Yi

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