**Q.8. What are regression lines?**

**Ans.** The lines which give the best estimate of the value of one variable for any given value of the other variable are called the ‘Lines of regression’ or ‘Regression lines’. In other words, regression lines are used to predict the value of the dependent variable when the value of the independent variable is known.

**Q.9. Write the three functions of regression lines. **

**Ans.** The three functions of **regression lines** are:

- They indicate the degree and direction of correlation.
- They are useful in predicting the value of the dependent variable when the value of the independent variable is known.
- They are helpful in the calculation of mean value as the perpendiculars drawn at the point where the two regression lines cut each other are the mean value of the two variables.

**Q.10. Define the regression equation of X on Y.**

**Ans.** The regression equation of X on Y describes the variations in the values of X for the given changes in the values of. In other words, this equation is used for estimating or predicting the value of X for a given value of Y. This equation is expressed as follows:

When the coefficient of correlation (Y) and standard deviation (6) are given in the question, it can be easily calculated as

**Q.11. Define the regression equation of Y on X.**

**Ans.** The regression equation of Y on X describes the variations in the values of Y for the given changes in the values of X. In other words, this equation is used for estimating or predicting the value of Y for a given value of X. This equation is expressed as follows:

When the coefficient of correlation (Y) and standard deviation (0) is given in the question, it can be easily calculated as

**Q.12. Define the term regression coefficient.**

**Ans.** The regression coefficient is an algebraic measure of the slope of the regression lines. It is for this reason that it is also known as the ‘Slope coefficient. Since there are two regression equations, there are two regression coefficients.

**Q.13. What do you mean by partial correlation?**

**Ans.** When we study the correlation among more than two variables, but in that study, we only consider the inter-relationship between two variables, and the third variable is assumed to be constant, the correlation is said to be a partial correlation.