1/17/2024 0 Comments To regress x on y![]() The assumption that what has happened in the past is a good indicator of what will happen in the future is a simplistic assumption. It is possible that there are other factors involved in the changes in the variables which may not have been considered.Īlso, like time series analysis, which is dealt with in a separate article, regression analysis uses past observations to attempt to predict what will happen in the future. The calculations performed can only suggest that a relationship exists between the factors, it cannot prove the relationship. ConclusionĬare must be taken however when using regression analysis and correlation to make future forecasts. This means that 6.9% of the changes must be due to other factors. In this example, r 2 = 0.931, so 93.1% of the changes in total production cost can be explained by changes in activity levels. The coefficient of determination gives the proportion of changes in y (the dependent variable) that can be explained by changes in x (the independent variable). R = 0.965 which indicates a strong positive correlation.Ī further calculation is the coefficient of determination which is calculated as r 2. Some other relationships are shown below: The chart shown in the ‘line of best fit’ section above shows a strong positive correlation. Correlation can be positive (where increases in one variable result in increases in the other) or negative (where increases in one variable result in decreases in the other). Two variables are said to be correlated if they are related to one another and if changes in one tend to accompany changes in the other. The stronger the relationship between the variables, the more reliance can be placed on the equation calculated and the better the forecasts will be.Ī measure of the strength of the relationship between the variables is correlation. How reliable this estimate is will depend on the strength of the relationship between the two variables how much of the change in y can be explained by the change in x? Using this equation, it is easy to forecast total costs at different levels of production, for example for a production level of 80,000 units, the estimate of total cost will be:Ģ08.90 + (9.1 x 80) = 936.90, or $936,900. The equation of the regression line (in the form y = a + bx) becomes: We assume a linear (straight line) relationship between the variables and that the equation of a straight line is:Ī is the fixed element (where the line crosses the y axis)ī is the variable element (gradient of the line) andĪ and b are calculated using the following formulae: Regression analysis also uses the historic data and finds a line of best fit, but does so statistically, making the resulting line more reliable. A method which can overcome this weakness is regression analysis. The main one being that the ‘line of best fit’ is estimated from the data points plotted and different lines may be drawn from the same set of data points. This is a straightforward technique, but it has some limitations. For levels of production which don’t fall within the range of the previous levels, it is possible to extrapolate the ‘line of best fit’ to forecast other levels by reading the value from the chart. This ‘line of best fit’ can be used to predict what will happen at other levels of production. In this case some of the points are on the line and some are above and below, but most are close to the line which suggests that there is a relationship between activity level and the total production cost. ![]() For example the total cost of a production process would be dependent on the level of activity.Ĭonsider the following data produced by a company over the last two years. In any relationship between two variables there is an independent variable and a dependent variable, the size of the movements in the dependent variable depending on the size of the movements of the independent variable. This article will look at how the relationships between variables can be analysed using the ‘line of best fit’ method and regression analysis, and how the strength of these relationships can be measured using correlation. This will be invaluable when budgeting or forecasting. Understanding these relationships allows organisations to make better predictions of what sales or costs will be in the future. For example, it would be useful to understand the relationship between advertising spend and sales generated from that advertising spend or between the production level and the total production costs. An introduction to professional insightsīeing able to understand the relationship between different factors is very important for organisations.Virtual classroom support for learning partners.Becoming an ACCA Approved Learning Partner. ![]()
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