Linear Regression

Linear Regression- The Statical Data Analysis technique that you should know

Regression, as the term implies, is the statistical technique where the path of greatest representation is chosen, and it is explained why a certain behaviour or outcome happened. To put simply, if you want to predict future action based on the data, linear regression is one of the most basic ways to do it, there are several other advanced variations of regression, however, for this topic, we will keep it limited to linear regression.

Regression is important because it established the causality, so to say, to can decompose factors that lead to action while also explaining the extent to which an outcome can vary when any input into the system is changed. For example, if the purchase decision of the consumer is based on price and design, regression not only confirms that it is indeed true that a relationship between variables exists in the real market place and how much will change on aspect affect the outcome of the purchase. The simplest example of this is, if I change my price by 10%, how much will my demand fall or grow?

At the heart of regression is causality. Normally, in statistics, when we want to know, if a relationship like a price and demand exists in the market, we do correlation analysis, to see if manipulation of one variable will affect the other variable, however, correlation doesn’t claim that it is because of each other, their outcomes vary. This is the regression’s strength, as it calculates that path, through which most people’s response can be explained. A 100 different people behaving in 100 different ways have commonalities which affect the outcome of their actions. and if they do, to what extent the regression reveals.

Linear Regression- What Is It?

We for starters, there is a hypothesis from the enquiring party, which should state theoretically why something should occur, like a demanding fall with the price rise. Normally, manipulation of one of the variables to maximize the profit, in this case, being the objective. So, the change in price effects, the demand for the product. In this case, the demand is called the predictor variable, and the price independent variable. What is being predicted is called the regression coefficient, which means the extent to which one-unit change will affect the other variable.

In real-life applications, usually, the equation is a great deal wider as it tries to encompass a phenomenon and its underlying nudges. In these cases, several independent variables go into the prediction of one dependent variable, case in point being, consideration for a brand. When a consumer is considering a brand, they take all the Ps and Cs of marketing and all the other inputs of marketing, advertising, media, branding, placement and pricing, each has a little or small impact on the overall consideration, except in some cases.

For decision-makers, who have the budgets to manipulate not all but some or in most cases just part of the marketing mix and are expected to produce results from focusing on that variable, also marketing and brand managers choose to focus on different triggering variables that result in an eventual desired action from the consumer. In these cases, the decision-makers, choose manipulation of their marketing resources in a way that they select one or two of the effecting factors and yet result in a huge increase in the desired result that is consideration or sale.

A live example of this is, a linear regression prediction can tell you, that if there is advertising, discounts, promos, media and retail budget, then by manipulating each with the same budget, what is the resulting delta in the consideration.

Technically, let’s understand Linear Regression !

If you plot your data on X, On Y scale you will see no commonality or pattern most of the times. Sometimes when you see, it is obvious and does not reveal much, at least for decision-makers. The idea of regression, in this case, is to be able to then come up with an equation which can most describe the impact of the independent variable (variance in the data), and the constant. The regression equation draws that line or gives that equation, i,ethe coefficient of regression, which explains how much change it can cause in the outcome.

The basic type of regression equations are with one dependent and one independent variable and is defined by the formula y = c + b*x, where y = estimated dependent variable, c = constant, b = regression coefficient, and x = independent variable.

The overall level it reveals two things:

1. How well does a set of independent variables account for the widest variance in the dependent variable?

2. Which variables are significant predictors of the dependent variable, and in what way do they–that is, magnitude indicated by the sign of coefficient?

Due to these properties, there are three major applications of regression analysis:

1. Determining the strength of independent variables

The regression identifies the magnitude of the effect the independent variable(s) have on a dependent variable. Typical questions are, what is the strength of the relationship between dose and effect, sales and marketing spend, and age and salary.

2. Forecasting an effect

Regression forecasts the effects or impact of changes. It reveals how much the dependent variable changes with a change in one or more independent variables. A typical question is, “how much additional sales do a campaign generate for each additional $1000 spent on marketing?”

3. Trend forecasting or time series forecasting.

Regression analysis predicts trends and future values. It is normally used to get point estimates. A typical application is, “what will the price of oil be in 6 months?

Technically, let’s understand Linear Regression !
Last but not least

The efficacy of your prediction in the real world will depend on the type of regression model was used for prediction. To start with, there are 6 types of linear regressions alone. These are simple linear, multiple linear, logistic regression, ordinal regression, discriminant analysis and multinomial analysis.

When selecting the model for the analysis, an important consideration is model fitting. Adding more independent variables to a linear regression model will always increase its R square, its ability to explain the variance, but having too many variables leave the decision-makers too many things to act on.

A professional describes the problem extremely well – a simple model is usually preferable to a more complex model. Statistically, if a model includes many variables, some of the variables will be statistically significant due to chance alone.

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