Calculation of covariance and simple linear models

 Covariance is a measure of the relationship between two random variables.
 A measure of the variance between two variables. However, the metric does
not assess the dependency between variables.
 The measure of the strength of the linear relationship between x and y is
called the covariance.

 Covariance is measured in units.
 The units are computed by multiplying the units of the two variables (x,y).
 The variance can take any positive or negative values.
 The values are interpreted as follows:
Positive covariance:
When two variables (x and y) move in the same direction (both increase or
both decrease) then covariance is, large and positive
Negative covariance:
When two variables (x and y) move in the opposite directions (one
increases while the other decreases) the covariance is a large negative number
 When there is no particular pattern the covariance is a small number

 The covariance formula deals with the calculation of data points from the
average value in a dataset.
 For example, the covariance between two random variables X and Y can be
calculated using the following formula (for population):
Where, Xi – the values of the X-variable
Yj – the values of the Y-variable
X̄ – the mean (average) of the X-variable
Ȳ – the mean (average) of the Y-variable
n – the number of data points

 A simple linear regression model is a mathematical equation that
describes the relationship between two or more variables.
 A simple linear model includes only two variables:
 one independent and one dependent.
 Dependent variable is the one being explained
 Independent variable is the one used to explain the variation in the
dependent variable.
 A (simple) linear model that gives a straight-line relationship between two
variables.

 In the model,
ŷ = a + bx, a and b, which are calculated using sample data, are
called the estimates of A and B.

Calculation of covariance and simple linear models

 The dependent (or response) variable is the variable needed to understand
or predict (usually the y term)
 The independent (or predictor) variable is the variable used to understand
or predict the dependent variable (usually the x term)
Linear Regression Analysis
 Its a statistical technique that uses observed data to relate the
dependent variable to one or more independent variables.
 The objective of regression analysis is to build a regression model (or
predictive equation) that can be used to describe, predict, and control the
dependent variable on the basis of the independent variable

Calculation of covariance and simple linear models

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