Statistics Standard 12>Chapter -1 - Regression Analysis>Exercise>Q 10

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12th Tamil Nadu Board

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Regression analysis helps in establishing a functional relationship between ______ variables.

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Important Points to Remember in Chapter -1 - Regression Analysis from Tamil Nadu Board Statistics Standard 12 Solutions

1. Regression analysis :

Regression analysis is a statistical method of determining relationship between independent variable and a dependent variable.

2. Types of Regression

(i) Simple linear regression :

If the relationship is linear and there is only one independent variable, then the regression is called as simple linear regression.

(ii) Multiple linear regression :

If the relationship is linear and the number of independent variables is two or more, then the regression is called as multiple linear regression.

(iii) Non-linear regression :

If the relationship between the dependent variable and the independent variable(s) is not linear.

3. General form of simple linear regression:

(i) In simple linear regression there are two linear regression lines.

(ii) In the linear regression line $Y = a + b X + e$ .

4. Relation between correlation coeficcient and regression coefficient :

$r_{X Y} = \sqrt{b_{X Y} b_{Y X}}$

5. General form of multiple linear regression:

$Y = a + b_{1} X_{1} + b_{2} X_{2} + b_{3} X_{3} + \dots + b t X_{t} + e$ .

6. Method of least squares:

(i) Sum of the residuals zero is $\sum_{i = 1}^{n} (y_{i} - {\hat{y}}_{l}) = 0$ .

(ii) Sum of the squares of the residuals is $E (a, b) = \sum_{i = 1}^{n} {(y_{i} - {\hat{y}}_{2})}^{2}$ .

7. Pearson’s coefficient and correlation coefficient:

$b_{X Y} = r_{X Y} \frac{S D (X)}{S D (Y)}$

8. Angle between the two regression lines:

$θ = \tan^{- 1} \frac{m_{1} - m_{2}}{1 + m_{1} m_{2}}$