ML Aggarwal Linear Regression ISC Class-12 Maths Solutions

ML Aggarwal Linear Regression ISC Class-12 Maths Solutions Chapter-2 of Section-C. Step by step Solutions of ML Aggarwal ISC Class 12 Mathematics for Exercise Questions with Chapter Test. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

ML Aggarwal Linear Regression ISC Class-12 Maths Solutions Cha-2 of Sec-C

Board	ISC
Class	12
Subject	Mathematics
Ch-2 of Sec-C	Linear Regression
Session	2024-25
Topics	Solutions of ML Aggarwal

Linear Regression

ML Aggarwal Linear Regression ISC Class-12 Maths Solutions Cha-2 of Sec-C

Linear Regression Equation: The measure of the extent of the relationship between two variables is shown by the correlation coefficient. The range of this coefficient lies between -1 to +1. This coefficient shows the strength of the association of the observed data for two variables. A linear regression line equation is written in the form of: Y = a + bX where X is the independent variable and plotted along the x-axis Y is the dependent variable and plotted along the y-axis The slope of the line is b, and a is the intercept (the value of y when x = 0).

Linear Regression Formula

Linear regression shows the linear relationship between two variables. The equation of linear regression is similar to the slope formula what we have learned before in earlier classes such as linear equations in two variables.

Simple Linear Regression

The very most straightforward case of a single scalar predictor variable x and a single scalar response variable y is known as simple linear regression. The equation for this regression is represented by; y=a+bx

The expansion to multiple and vector-valued predictor variables is known as multiple linear regression, also known as multivariable linear regression. The equation for this regression is represented by; Y = a+bX

Almost all real-world regression patterns include multiple predictors, and basic explanations of linear regression are often explained in terms of the multiple regression form. Note that, though, in these cases, the dependent variable y is yet a scalar.

Linear Regression Line

The most popular method to fit a regression line in the XY plot is the method of least-squares. This process determines the best-fitting line for the noted data by reducing the sum of the squares of the vertical deviations from each data point to the line. If a point rests on the fitted line accurately, then its perpendicular deviation is 0. Because the variations are first squared, then added, their positive and negative values will not be cancelled.

Properties of Linear Regression

For the regression line where the regression parameters b₀ and b₁ are defined, the properties are given as:

The line reduces the sum of squared differences between observed values and predicted values.
The regression line passes through the mean of X and Y variable values
The regression constant (b₀) is equal to y-intercept the linear regression
The regression coefficient (b₁) is the slope of the regression line which is equal to the average change in the dependent variable (Y) for a unit change in the independent variable (X).