# OP Malhotra Linear Regression ISC Class-12 Maths Solutions Ch-27

OP Malhotra **Linear Regression** ISC Class-12 Maths Solutions Ch-27. Step by step Solutions of OP Malhotra SK Gupta, Anubhuti Gangal S.Chand ISC Class-12 Mathematics with Exe-27 Self Revision and Chapter Test. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

## OP Malhotra Linear Regression ISC Class-12 Maths Solutions Ch-27

Class: | 12th |

Subject: | Mathematics |

Chapter : | Ch-27 Linear Regression of Section -C |

Board | ISC |

Writer | OP Malhotra, SK Gupta, Anubhuti Gangal |

Publications | S.Chand Publications 2020-21 |

**-: Included Topics :-**

Exe-27

Self Revision

Chapter Test

### OP Malhotra Linear Regression ISC Class-12 Maths Solutions Ch-27

**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. It is given by:

Y= a + bX

**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.

**Properties of Linear Regression :-**

**For the regression line where the regression parameters b _{0} and b_{1} 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 (b
_{0}) is equal to y-intercept the linear regression - The regression coefficient (b
_{1}) 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).

Exe-27

### OP Malhotra Linear Regression ISC Class-12 Maths Solutions Ch-27

### Self Revision

OP Malhotra Linear Regression ISC Class-12 Maths Solutions Ch-27

### Chapter Test

OP Malhotra Linear Regression ISC Class-12 Maths Solutions Ch-27

**-: End of Linear Regression ****S. Chand ISC Class-12 Maths Solution :-**

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