Flash Education

Generic selectors
Exact matches only
Search in title
Search in content
Post Type Selectors
post
question

Linear Regression | Class 12 Mathematics Formula

Linear-Regression-formula

Linear Regression

Linear regression is a statistical method used to model the relationship between a dependent variable 𝑦 and one or more independent variables 𝑥 by fitting a linear equation of the form:

Types of Lines of Regression:

  1. Line of Regression of y on x
  2. Line of Regression of x on y

Line of Regression of y on x

Equation y – ȳ = byx(x – x̄)
(i) Mean of x (x̄) = ∑x/n
(ii) Mean of y (ȳ) = ∑y/n
(iii) byx = ∑\text{xy} - {1\over n}∑\text{x}∑\text{y}\over ∑\text{x}^2 - {1\over n}(∑\text{x})^2
= \text{cov(x,y)}\over \text{var (x)}
= \text{cov(x, y)}\over  \text{σ}_\text{x}
= r\text{σ}_\text{y}\over \text{σ}_\text{x}
= ∑\text{(x - x̄)(y - ȳ)}\over ∑\text{(x - x̄)}^2
= ∑\text{uv} - {1\over n}∑\text{u}∑\text{v}\over ∑\text{u}^2 - {1\over n}(∑\text{u})^2

Line of Regression of x on y

Equation x – x̄ = byx(y – ȳ)
(i) Mean of x (x̄) = ∑x/n
(ii) Mean of y (ȳ) = ∑y/n
(iii) byx = ∑\text{xy} - {1\over n}∑\text{x}∑\text{y}\over ∑\text{y}^2 - {1\over n}(∑y)^2
= \text{cov(x,y)}\over \text{var (y)}
= \text{cov(x, y)}\over  \text{σ}_\text{y}
= r\text{σ}_\text{x}\over \text{σ}_\text{y}
= ∑\text{(x - x̄)(y - ȳ)}\over ∑\text{(y - ȳ)}^2
= ∑\text{uv} - {1\over n}∑\text{u}∑\text{v}\over ∑\text{v}^2 - {1\over n}(∑\text{v})^2

Properties of Lines of Regression

  1. bxy, byx and r or ρ (x, y) are of same sign
  2. Square of Coefficient of correlation (r2) = bxy. byx
  3. 0 ≤ bxy. byx ≤ 1 or 0 ≤ r2≤ 1
  4. If one of bxy. byx is numerically greater than one, the other is numerically smaller than one.
  5. The two regression lines intersect at (x̄, ȳ)
  6. If r = 0, then the lines of regression are parallel to the coordinate axes.
  7. The angle between two regression lines (θ) is given by tan  θ = |{1 - \text{r}^2\over \text{b}_{\text{xy}} + \text{b}_{\text{yx}}}|

≫ You May Also Like

Close Menu
error: Content is protected !! 💀
Index