# Regression Analysis

Regression Analysis is a statistical technique for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function of the independent variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function, which can be described by a probability distribution.

Regression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning. Regression analysis is also used to understand which among the independent variables are related to the dependent variable, and to explore the forms of these relationships. In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables. However this can lead to illusions or false relationships, so caution is advisable. For example, correlation does not imply causation.

A large body of techniques for carrying out regression analysis has been developed. Familiar methods such as linear regression and ordinary least squares regression are parametric, in that the regression function is defined in terms of a finite number of unknown parameters that are estimated from the data. Nonparametric regression refers to techniques that allow the regression function to lie in a specified set of functions, which may be infinite-dimensional.

The performance of regression analysis methods in practice depends on the form of the data generating process, and how it relates to the regression approach being used. Since the true form of the data-generating process is generally not known, regression analysis often depends to some extent on making assumptions about this process. These assumptions are sometimes testable if many data are available. Regression models for prediction are often useful even when the assumptions are moderately violated, although they may not perform optimally. However, in many applications, especially with small effects or questions of causality based on observational data, regression methods can give misleading results.

### Usage of Regression Analysis

Regression analysis can predict the outcome of a given key business indicator (dependent variable) based on the interactions of other related business drivers (explanatory variables). For example: it allows you to predict sales volume, using the amount spent on advertising and the number of sales people that you employ. Of course, a real model would need more variables and is much more complex.

Nobody can really see into the future. However modern statistical methods, econometric models and business intelligence software can be used to forecast and estimate what is going to happen in the future.

Regression Analysis models are used to help us predict the value of one unknown variable, through one or more other variables whose values can be predetermined.

### Steps in Regression Analysis

The first stage of the process is to identify the variable that we must predict (the dependent variable). Then we carry out multiple regression analysis, focusing on the variables we want to use as predictors (explanatory variables). The multiple regression analysis would then identify the relationship between the dependent variable and the explanatory variables. This is then finally presented as a model (formula).

Regression Analysis in Excel

Microsoft Excel is often used to for modeling and has many in-built functions to perform regression analysis.  These are the functions:

• For Linear Regression: LINEST, TREND, FORECAST, SLOPE, STEYX
• For Exponential Regression: LOGEST, GROWTH

These functions are entered as array formulas and they produce array results. You can use each of these functions with one or several independent variables. The following list provides a definition of the different types of regression:

• Linear Regression produces the slope of a line that best fits a single set of data. Based on a year’s worth of sales figures, for example, linear regression can tell you the projected sales for March of the following year by giving you the slope and y-intercept (that is, the point where the line crosses the y-axis) of the line that best fits the sales data. By following the line forward in time, you can estimate future sales, if you can safely assume that growth will remain linear.
• Exponential Regression produces an exponential curve that best fits a set of data that you suspect does not change linearly with time. For example, a series of measurements of population growth will nearly always be better represented by an exponential curve than by a line.
• Multiple Regression is the analysis of more than one set of data, which often produces a more realistic projection. You can perform both linear and exponential multiple regression analyses. For example, suppose you want to project the appropriate price for a house in your area based on square footage, number of bathrooms, lot size, and age. Using a multiple regression formula, you can estimate a price, based on a database of information gathered from existing houses.