Regression attempts to model the relationship between a dependent variable (Y) and one or more independent variables (X). It provides an equation to estimate or predict the average value of Y based on the value(s) of X. The document then discusses single and multiple regression, the concept of a least squares regression line in the form of Y = a + bX, and provides an example to calculate the regression coefficients a and b and the regression line using a dataset with one dependent (Y) and independent (X) variable. The estimated regression line from the example is Y = 1.47 + 2.831X, where b=2.831 indicates that Y increases by 2.831 units for each one unit increase in X
2. Investopedia defines
Regression as ‘A statistical
measure that attempts to
determine the strength of
the relationship between
one dependent variable
(usually denoted by Y) and a
series of other changing
variables (known as
independent variables).’
3. Concept of
Regression
It investigates the dependence of one variable,
conventionally called the dependent variable, on one or
more other variables, called independent variables.
It then provides an equation to be used for estimating or
predicting the average value of the dependent variable
from the unknown values of the independent variable.
The relation between the expected value of the
dependent variable and the independent variable, is
called a regression relation.
4. Concept of
Regression
(Contd.)
The dependence of a variable on a single
independent variable, is called a single or two-
variable regression.
The dependence of a variable on two or more
independent variable, is called multiple
regression.
Regression is represented by a straight line
equation, and said to be linear regression.
10. Least Squares
Regression
Line
𝒀 = 𝒂 + 𝒃𝑋
(Where a & b are Regression Coefficients)
Dependent Variable
Independent
Variable
Intercept
slope
b =
𝑛∑𝑋𝑌−(∑𝑋)(∑𝑌)
𝑛∑𝑋2 − ∑𝑋 2
𝑎 = 𝑌 − 𝑏 𝑋
11. Example
X 5 6 8 10 12 13 15 16 17
Y 16 19 23 28 36 41 44 45 50
Compute the least squares regression equation
of Y on X for the following data. What is
regression coefficient and what does it mean?
We Know, the estimated regression line of Y on X is
𝑌 = 𝑎 + 𝑏𝑋