ACCA Paper F2 free course note | Correlation & Regression | Regression Equation

Regression equation is an equation that expresses the linear relationship between two variables. It is an algebraic expression of the regression line. Since there are two regression lines, there are two regression equations—the regression equation of X on Y is used to describe the variations in the values of X for given changes in Y and the regression equation of Y on X is used to describe the variations in the values of Y for given changes in X.

Regression equation of Y on X

The regression equation of Y on X is expressed as follows:

                Y= a + bX

Where Y is the dependent variable to be estimated and X is the independent variable. The parameter ‘a’ determines the level of the fitted line. The parameter ‘b’ determines the slope of the line, i.e., the change in Y for unit change in X.

                b =

               

                a = - b

Regression equation of X on Y

The regression equation of X on Y is expressed as follows:

                X= a+ bY

 The parameter ‘a’ determines the level of the fitted line. The parameter ‘b’ determines the slope of the line, i.e., the change in X for unit change in Y.

                b =

               

                a = - b

Illustration: Calculate the regression equation of Profit on Capital and Capital on Profit from the following data.

Capital (X)	Profit (Y)
5	2
10	3
15	5
20	8
25	12

ACCA Paper F2 free course note | Correlation & Regression | What is Regression

The dictionary meaning of the term “regression” is the act of returning or going back. The term “regression” was first used in 1877 by Francis Galton while studying the relationship between the height of fathers and sons.

Regression analysis is the technique used to develop the equation and provide the estimate. In regression, we develop an equation to express the linear relationship between two variables. In addition, we are able to estimate the value of the dependent variable Y based on a selected value of the independent variable X.

The statistical tool with the help of which we are in a position to estimate (or predict) the unknown values of one variable from known values of another variable is called regression.

With the help of regression analysis we are in a position to find out the average probable change in one variable given a certain amount of change in another variable.

For example, if we know that advertisement and sales are correlated, we may find out the expected amount of sales for a given advertisement expenditure or the required amount of expenditure for achieving a fixed sales target.

Differences between correlation and regression analysis

There are two important points of difference between correlation and regression analysis. These are

v  Correlation coefficient measures the degree of association between two or more than two variables, whereas regression analysis measures the nature of relationship between the variables.

v  In case of correlation analysis, it never measure cause and effect relationship whereas regression analysis specially measures this.

Regression Line

Regression line is the graphical presentation of equation. It is a line drawn through a scatter plot of two variables If we take the case of two variables X and Y, we shall have two regression lines as the regression line of X on Y and the regression line of Y on X. 

ACCA paper F6 UK Basic Income Tax computation | Tax reliefs & Qualifying interest payments

Tax reliefs

Tax relief is given for certain losses incurred (e.g. trading losses and certain qualifying interest payments).

Qualifying interest payments

·         Purchase of a share in a partnership

·         Purchase of ordinary shares in, or loans to a close trading company (controlled by 5 or fewer)

·         Purchase of ordinary shares in an employee controlled UK resident unquoted trading company

·         Purchase of plant & machinery by an employee for use in his employment

·         Payment of inheritance tax by a personal representative of a deceased’s estate

Interest not allowed

·         Interest on debts used to finance expenditure for trade purpose

·         Interest incurred on borrowings to acquire or improve commercial letting property

·         To provide working capital for a letting trade