# Regression Analysis: Find the Best Fit for your Statistical Model

Regression analysis investigates the relationship between variables; typically, the relationship between a dependent variable and one or more independent variables. It’s used for many purposes like forecasting, predicting and finding the causal effect of one variable on another. For example, the effects of price increase on the customer’s demand or an increase in salary causing a change in spending etc. Regression techniques basically involve the assembling of data on the variables under study and estimating the quantitative effect that they have on the other variables. While conducting regression, you must be careful to investigate the nature of the relationship too – whether it’s a true relation or a false one and also assess the significance of the relation to the analysis being done.

If you are a statistician or analyst, a student or professional, you will find regression analysis is an important tool for modelling and analyzing data (this course can show you how to create a regression model in no time!) In today’s tutorial, we will discuss the various types of regression methods and their features, touch upon the process of choosing an appropriate method of analysis and understand the tool with the help of an example.

## What is Regression Analysis?

In its most simple definition, regression analysis is defined as a statistical tool that explores the relationship between a dependent variable and one or more independent variables. It studies the quantitative effect of a variable on another and investigates their relationship for further analysis. Learn more about regression analysis in our introductory course on statistical analysis.

**Why Use Regression Analysis?**

Unlike the other statistical tools, regression analysis takes into account the risks of making assumptions and easily addresses the most complicated of problems due to its flexibility. It considers the significance of each variable and what effect they have on each other, while solving the trickiest of situations. The many features of regression analysis that make it a popular tool are:

- Can handle multiple co-related predictor variables
- Used for continuous and categorical variables
- Addresses unknown parameters
- Studies the effect of one predictor variable on a dependent variable
- Higher-order terms can be used for modelling and data analysis

While conducting a research, often you’ll be faced with a number of entangled co-related variables that can all affect the dependent variable in their own way. At times like this, regression analysis is the most useful as it studies the variables individually and determines their significance with greater accuracy. Say, for example, you want to find out the effect of protein shakes and exercise on the weight of a person undergoing a fitness program. Or you want to study the relationship between salaries and qualification on the job performance of an employee. These studies will naturally involve a lot of co-related variables that will individually have an effect on the dependent variable. These complex questions can be easily answered with the help of regression analysis – this course on variance analysis with SPSS shows you exactly how.

There are many kinds of regression techniques, but it’s important for you to choose the best method to suit your research. To find out more about the benefits and usage of regression analysis, check our introduction to SPSS Training and Tools.

## Types of Regression Techniques

There are a number of statistical software solutions that provide different kinds of regression techniques such as:

**Linear Regression**

This is a simple and easy to use method that models the relationship between a dependent variable y and one or more explanatory variables denoted as X. If it’s only one explanatory variable, then it becomes a case of **Simple Linear Regression** whereas when there are multiple explanatory variables, it’s called **Multiple Linear Regression. **This method uses linear predictor functions for data modelling wherein unknown parameters are estimated from the data. The technique focuses mainly on the conditional probability distribution of y with respect to X and can be used in a lot of practical applications. Since linear models are linearly dependent on unknown parameters, they are easier to fit than non-linear models and lead to easier determination of statistical parameters.

**Least Squares Method**

The method of least squares is used to analyze and solve over determined systems (sets of equations wherein the equations are more than the unknowns). It’s best suited for data fitting applications such as fitting a straight line on to the points in a scatter diagram etc. Since it minimizes the sum of squared residuals (residual is nothing but the difference between observed value and fitted value), the overall solution reduces the sum of squares of the errors in each equation. This method can be used for linear as well as non-linear regression depending on the nature of the residuals and equations.

**Non-Linear Regression**

The non-linear regression analysis uses the method of successive approximations. Here, the data are modeled by a function, which is a non-linear combination of model parameters and depends on one or more explanatory variables. Therefore, in non-linear regression too, the models could be based on simple or multiple regressions. Non-Linear Regression is best suited for functions like exponential, trigonometric, logarithmic, power or Gaussian functions and fitting curves like the Lorenz curves, exponential curves etc. This method takes into account the nature of relationship between the variables and tries to find some kind of transformation in them so that the relationship can be expressed easily as a straight line. In case the relationship is not clear, then you must approach the problem by resorting to a scatter diagram so that you can analyse the probable transformations before building an appropriate model.

## Selecting the Regression Technique and Models

While there are a variety of regression tools and techniques for statistical analysis, it’s important to choose the right one depending on the characteristics of the data at hand. Keep these important points in mind while selecting the regression analysis technique:

- Prior to selecting the technique or model, find out the importance of the different variables, their relationships, coefficient signs and their effect by conducting thorough research.
- To determine the goodness of fit of the model, you need to analyse the coefficients of determination, measure the standard error of estimate, analyse the significance of regression parameters and confidence intervals. Better fits lead to more precision in the results.
- Remember, simple models produce more accurate results; so while the problem might be complex, it’s not always necessary to adopt a complex model. Start with simple models by breaking down the problem and add complexity only when required.
- Tread cautiously while inferring causal relationships; always remember the mantra- ‘correlation does not imply causation’.

## Regression Analysis Example

Let’s try to understand regression analysis with a help of a simple example wherein we will study the relationship between agricultural yields with respect to amount of fertilizer used. The process of regression analysis will involve the following steps:

- Study the different fertilizer inputs vs the yield based on data collected from the field.
- Draw a scatter diagram to establish the relationship between the two variables, fertilizer input (X) and agricultural yield (y). The diagram will give an idea on the nature of relationship – whether it’s a straight line or curve.
- Depending on the characteristic of the scatter diagram, adopt a linear or non-linear model and fit the data accordingly.
- Evaluate your model and use it for prediction or forecasting.

This course on descriptive statistics in SPSS can help you understand this better.

Whether it’s in business or research, analysts need to study huge amounts of data to find solutions to the most complex of problems. Regression Analysis helps you to study several independent variables, their relationships and the effects they have on dependent variables easily. In short, a good regression analysis needs sound reasoning and proper interpretation of data for highly accurate predictions, forecasts and solutions!

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