Whether you’re a sales manager hoping to predict your sales for the coming quarter, a project manager studying the relationship between academic and job performance or a company CEO looking to predict growth for your organization, regression analyses can be an efficient and reliable method to model and analyze data. As with any predictive modeling technique, you’re likely to be making critical decisions based on what the data suggests, so you need to make sure you can rely on the output you get.
For instance – perhaps you’re forecasting or hoping to find the causal relationship between two variables. Or, you’re doing time series modeling and you’ve just completed a regression analysis. You have painstakingly made sure that you’ve got everything right, but the results seem to jump out at you as incomprehensible, illogical or even downright wrong. What happened here?
No matter whether we’re working with small-scale data sets or complex models, there is a margin for error based on some simple mistakes or overlooked aspects. From start to finish, there are many different steps in carrying out a regression analysis. From data collection and entry, to model specification and interpretation, there is a chance of error at multiple stages. In this explainer, we outline the different sources of regression errors and methods to correct them, to help you achieve a regression result that has a high degree of accuracy and certainty with a minimal error term.
Check for errors in data collection and entry
The first thing to do if you’ve got a lopsided result on your hands is to verify the data that was collected and inputted. When it comes to data collection, remember that bad data can have a disproportionate impact on your analysis. If the data that’s been gathered seems suspicious or unreliable, you may want to consider starting with a clean state – regression analyses are highly sensitive to the quality of data.
Even if you’ve been careful in putting together the database, there could be small or overlooked errors in data coding and entry that affect your results. Even a minimal number of data points that are impossible or extreme can lead to faulty relationships in your analysis. Make sure you’ve reverse coded any negative errors, and look out for any errors at the data input stage itself.
Take care of avoiding any misspecification in your model
One of the most common mistakes that even experienced data scientists and statisticians sometimes make is model misspecification. Consider the functional relationship that exists between your chosen variables, and ensure that you set up your model properly by defining the response and predictor variables. If not, you will not be able to control what is being tested through your data model. There could be other relevant predictor variables that you’ve overlooked or missed,
Make sure you pick the right regression model
When you’re using a predictive modelling technique based on regression, there is a simple thumb rule that you can keep in mind. Is your family of variables discrete or continuous? Linear regressions work best for a continuous outcome, while logistic regressions should be chosen for a binary one.
Based on the data dimensionality and other characteristics, you may need to do some more homework. Check for possible bias in your model by using Mallow’s Cp criterion, or employ cross-validation to get an estimate for prediction accuracy. High dimensionality can be dealt with by using the appropriate regularization methods. Avoid multi collinearity and don’t correlate any independent variables with each other. Such a case can make it incredibly difficult for your model to make any accurate predictions about functional relationships.
While the Ordinary Least Squares (OLS) method is the most commonly used for minimizing the sum of squared errors, it may not always be the most appropriate choice. Consider other methods such as least absolute deviation, total least squares or generalized least squares, based on your requirements.
Consider whether you may be misinterpreting your results
If the data seems in place, then the other aspect to consider is your reading of the results. Make sure you understand the statistical software package you’re using, and go through the manual carefully to see if you’ve overlooked anything. If you’re using a new package, some of the techniques may differ from what you’re used to. Even within a single package, default options are sometimes different across different processes.
Correlation does not imply causation
Analyze your regression model and check to make sure your regression coefficients have not gotten reversed or changed. This can happen when you include an interaction term in your model.
It is also important to remember the popular saying – correlation does not imply causation. This couldn’t be truer than in the case of regression analysis, and we need to remember that a strong correlation result does not necessarily mean that a functional relationship exists between two or more variables. Let’s take a simple example – the sale of umbrellas may go up every year in the rainy season, just as the sale of icecream reduces. In both cases, it is a hidden variable – the season – that is the likely cause, but a monotonical relationship between these two variables may suggest causality. There is a fair bit of subjectivity involved in taking this call while running a predictive analysis through regression, so make sure you understand the problem at hand well to be able to understand this critical differentiation.
Understand how to interpret the Coefficient of Determination
R Squared, or the coefficient of determination, acts as a measure of the spread of data points around a regression line. Don’t make the common mistake of simply assuming that a high coefficient of determination indicates higher accuracy, as that is not always the case. While it is true that a high coefficient of determination can often lead to small standard errors, it can be misleading at times. Since R Squared is determined based on the sample under consideration, it can become inflated because of other reasons, such as a large number of predictor variables. Making use of an F-test is one way to estimate the significance of a regression coefficient.
Leave room for uncertainty
Last of all, remember that there is always room for uncertainty. Especially in regression analysis, the very existence of an error term is proof that any kind of prediction is just that – a prediction. The best way to get to a result that is as accurate as possible, is to minimize your error term. So, make sure that you improve you prediction as much as possible, by exploring interactions, looking for non-linearity in the terms or adding on additional predictors to your model. At the end of the day, the regression line with the fewest summed errors can be considered your most accurate result.
Other points to keep in mind
- Autocorrelation in error terms can also affect your standard error values.
- Make sure that there is a normal distribution for your error term and your dependent variable.
- Avoid Heteroscedasticity by ensuring constant variance in your error terms.
- Try not to overfit or underfit your model, for best results.
- Test your assumptions by plotting your data – a U-shaped or funnel-shaped pattern in an instant indicator that something is off.
In today’s data-driven world, it’s imperative to use data to influence your strategy and decision-making. But the best data scientists, organization leaders and managers combine high-quality data analysis with sound judgement and a little bit of intuition. When you get that balance right, it can make all the difference.
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