Linear Regression Analysis
Linear regression analysis is based on working out an equation for the line of best fit.
The line of best fit will be of the form
y = a + bx
y is the value of the dependent variable (on vertical axis)
a is the intercept - fixed costs
b is the slope of the line - variable costs
x is the value of the independent variable (on horizontal axis)
i. How do we calculate 'a' and 'b'?
How do we calculate ‘a’ and ‘b’?
‘a’ is the fixed cost per period
‘b’ is the variable cost per unit
‘x’ is the activity level (independent variable)’
‘y’ is the total cost = fixed cost + variable cost
‘n’ is the sample size – number of pairs of data
These formulae are given in the exam. Remember always start working ‘b’, then move to ‘a’.
Correlation measures the strength of the relationship between two variables.
One way of measuring ‘how correlated’ two variables are, is by drawing the ‘line of best fit’ on a scatter graph. When correlation is strong, the estimated line of best fit should be more reliable.
Another way of measuring ‘how correlated’ two variables are, is to calculate a correlation coefficient, r.
Different degrees of correlation
The correlation coefficient (r)
The correlation coefficient measures the strength of a linear relationship between two variables. It can only take on values between -1 and +1.
r = +1 indicates perfect positive correlation
r = 0 indicates no correlation
r = -1 indicates perfect negative correlation
The correlation coefficient is calculated as follows
This formula is also given in the exam
Coefficient of determination (r2)
The coefficient of determination is the square of the correlation coefficient.
It measures how much of the variation in the dependent variable is ‘explained’ by the variation of the independent variable.
The value of r2 can be between 0 and 1.
For example, if r = 0.97, r2 = 0.94 or 94%.
94% of the variation in the dependent variable (y) is due to variations in the independent variable (x). 6% of the variation is due to random fluctuations.
Therefore, there is high correlation between the two variables.