Managament accounting

partly correlated or uncorrelated. Correlation can be positive or negative.

Positive correlation means that low values of one variable are associated with low values of the other, and high values of one variable are associated with high values of the other.

Negative correlation means that low values of one variable are associated with high values of the other, and high values of one variable with low values of the other.

The correlation coefficient. The degree of linear correlation between two variables is measured by the Pearsonian (product moment) correlation coefficient, r. The nearer r is to +1 or –1, the stronger the relationship.

Correlation in a time series. Correlation exists in a time series if there is a relationship between the period of time and the recorded value for that period of time. The correlation coefficient is calculated with time as the X variable although it is convenient to use simplified values for X instead of year numbers. For example, instead of having a series of years 20X1 to 20X5, we could have values for X from 0 (20X1) to 4 (20X5).

Note that whatever starting value you use for X (be it 0, 1, 2 ... 721, ... 953), the value of r will always be the same.

The coefficient of determination, r2. The coefficient of determination, r2 (alternatively R2) measures the proportion of the total variation in the value of one variable that can be explained by variations in the value of the other variable. It denotes the strength of the linear association between two variables.

if the correlation coefficient between a company's output volume and maintenance costs was 0.9, r2 would be 0.81, meaning that 81% of variations in maintenance costs could be explained by variations in output volume, leaving only 19% of variations to be explained by other factors (such as the age of the equipment).

Note, however, that if r2 = 0.81, we would say that 81% of the variations in y can be explained by variations in x. We do not necessarily conclude that 81% of variations in y are caused by the variations in x. We must beware of reading too much significance into our statistical analysis.

Dependent and independent variables. If you are given two variables, the question might not tell you which is x and which is y. You need to be able to work this out for yourself.

y is the dependent variable, depending for its value on the value of x. x is the independent variable whose value helps to determine the corresponding value of y. Time is usually an independent variable.

For example, the total cost of materials purchases depends on the budgeted number of units of production. The number of production units is the independent variable (x) and the total cost is the dependent variable (y).

Estimating the equation of the line of best fit. There are a number of techniques for estimating the equation of a line of best fit. We will be looking at simple linear regression analysis. This provides a technique for estimating values for a and b in the equation Y = a + bx where X and Y are the related variables and a and b are estimated using pairs of data for X and Y.

Linear regression analysis (the least squares method) is one technique for estimating a line of best fit. Once an equation for a line of best fit has been determined, forecasts can be made.