What is Simple Linear Regression?
The simple linear regression is a linear regression model which has a single explanatory variable. It has two-dimensional sample points with one independent variable (x) and one dependent variable (y) and finds a linear function that is accurate and predicts the dependent variable values as a function of the independent variable.
Regression analysis is one of the commonly used analysis models that identifies and characterises relationships among multiple factors.
Simple Regression Equation Line:
The formula used for calculating simple linear regression is:
- y = predicted value of the dependent variable (y) for any given value of the independent variable (x).
- B0 = intercept, the predicted value of y when the x is 0.
- B1 = regression coefficient – how much we expect y to change as x increases.
- x = independent variable ( the variable we expect is influencing y).
- e = error of the estimate, or how much variation there is in our estimate of the regression coefficient.
Formulae:
Where,
m= sample size
ybar= mean of y
Xbar = mean of x
Assumptions:
- Linearity: The relationship between independent and the dependent variables is linear.
- Homoscedasticity: The variance of residual is the same for any value of independent variables .
- Independence: Observations are independent of each other.
- Normality: For any fixed value of independent and the dependent variables is normally distributed.
How to process with simple linear regression?
In statistical evaluation of research data, there is often need to describe relationships between two variables. This relationship is analysed through regression.
Example: 1) A university medical centre is investigating the relationship between stress and blood pressure. Assume that both a stress test score and a blood pressure reading have been recorded for a sample of 20 patients
Scatterplot With Regression Line:
Values of the independent variable, stress test score, are given on the horizontal axis, and values of the dependent variable, blood pressure, are shown on the vertical axis. The line passing through the data points is the graph of the estimated regression equation:
ŷ = 42.3 + 0.49x.
The parameter estimates, b0 = 42.3 and b1 = 0.49, were obtained using the least squares method.
A primary use of the estimated regression equation is to predict the value of the dependent variable when values for the independent variables are given.
Prediction using Regression equation:
For instance, given a patient with a stress test score of X=60, the predicted blood pressure is Y= 42.3 + 0.49(60) = 71.7.
Reference
Britannica, T. Editors of Encyclopaedia (2020, July 6). estimated regression equation. Encyclopedia Britannica. https://www.britannica.com/science/estimated-regression-equation