As businesses collect more data through advances in technology, business managers have improved opportunities to make data-driven decisions. A regression analysis is a useful tool in the hands of a capable manager. By describing the relationship between different variables, regressions can help you understand how your business works and make useful predictions about its evolution. Companies around the world use regressions for applications such as understanding the impact of oil prices on profitability or the effect of economic growth on sales as well as making predictions about stock prices and currency exchange rates.
One of the fundamental applications of regression analysis is to understand how much an independent variable affects a dependent variable. For example, you might be interested in justifying your company's advertising budget to your boss. By running a regression analysis of advertising expenditures (the independent variable) and company sales (the dependent variable), you can determine an equation that describes the relationship between them, such as sales = 100,000 + (5 times advertising expenditure). In other words, for each dollar spent on advertising, the company's sales increased by five times as much. An important caveat to consider is the regression's coefficient of multiple determination, or R^2, which indicates the strength of the relationship on a scale from zero to one. Higher values of R^2 indicate a stronger relationship between the variables, while lower values suggest a weaker relationship.
Regression analysis is also useful in testing hypotheses. For example, if your company is experiencing a slump in sales, the CEO might call a meeting of the heads of each department to identify the problem. You can examine all variables raised in the discussion by running a multiple regression analysis. For instance, you might run an analysis on the historical data of sales and advertising expenditures, number of sales staff and the mix of urban versus suburban stores. By simply adding or removing one variable from the model at a time, you can determine its explanatory effect on the sales decline by noting increases and decreases to R^2.
Often, you'll be more interested in the future than in the past. Regression analysis enables you to take advantage of historical data to extrapolate future outcomes. For example, if your boss wanted to know how much a $1 million increase in your advertising budget would impact sales, you could consult the regression equation for these two variables to make a confident prediction. In our earlier example, where sales = 100,000 + (5 times advertising expenditure), you'd expect a $1 million increase in advertising to generate $5 million of additional sales.
While powerful, regression analysis has some limitations. If you can't plot a straight line to express the relationship of the variables, then the usefulness of the regression is limited. Further, it's often difficult to distinguish between causation and correlation. For example, even though a regression analysis might indicate that increasing advertising expenditures are responsible for increasing sales with a high R^2 factor, the truth may be that other factors, such as rapid economic growth, are actually responsible. The challenge is to select the right variables for inclusion in the model.
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