Linear Regression with one independent variable
Linear regression, also known as linear least squares, models the straight-line relationship between the dependent variable and the independent variable.
In a simple linear regression, we may use a single independent variable to make predictions about the dependent variable. The regression line fits through the point corresponding to the means of the dependent and the independent variables. We may also test hypotheses about the relation between these two variables in addition to quantify the strength of the relationship.
We may run regression using two primary types of data: time series and cross-sectional.
Cross-sectional data engage many observations (relating to different asset classes, companies, people, countries or other entities) on X and Y for the same time period.
Whereas, time-series data involve many observations from different time periods for the same asset class, company, person, country or other entity. A mix of time-series and cross-sectional data is known as panel data.
Linear regression chooses values for coefficients b 0 and b 1 such that sum of the squared vertical distance between the observations and regression line is minimized.
Equation : Yi = b 0 + b 1x i + εi
Y : Dependent Variable (the variable that you are seeking to explain)
b 0 : Intercept
b 1 : Slope Coefficient
X : Independent Variable (the variable you are using to explain changes in the dependent variable)
ε : Error Term
1- Linear Relationship between variables.
2- The independent variable X is not random.
3- The expected value of the error term is zero.
4- The variance of the error term is the same for all observations.
5- The error term is uncorrelated across observations.
6- The error term is normally distributed.
If these assumptions are violated, the estimated regression coefficients (b^0, b^1) will be biased and inconsistent.
You might try to explain inflation (the dependent variable) as a function of growth in a country’s money supply (the independent variable).
Our calculator shows the average annual growth rate in the money supply (denoted x i ) and the average annual inflation rate (denoted Yi ) from 1980 to 2012 for the six countries (n = 6).
The equation to be estimated is
Long-term rate of inflation = b 0 + b 1 (Long-term rate of money supply growth) +ε.
Create a regression model to know how much variation in the long-term rate of inflation is explained by the long-term rate of money supply growth across the countries between 1980 and 2012.
Also predict the inflation rate if the long-term money supply growth rate is assumed to be 10% for any particular country.