# 5 Myths of Multiple Regression Analysis

Today’s world is data-driven, hence, you should always make decisions driven by data whenever possible. But processing the huge data volumes at your disposal isn’t easy. You mustn’t process the data manually. You can use a data analysis technique called *multiple linear regression.*

It helps data analysts to sort variables mathematically and identify those with an impact. Sample questions answered are:

Which variables matter most?

What variables can be removed?

What’s the relationship between these variables?

In this tutorial, we’ll discuss multiple regression in detail.

## What is Multiple Regression?

Multiple regression’s an advanced form of simple regression.

It predicts a variable’s value using 2/more variables.

The dependent variable (target variable) is the one whose value is to be predicted.

The *independent *variables (predictor variables) are those used for prediction.

The multi regression analysis determines the fitness of your regression model and the individual variable’s contribution to variance.

Prediction of exam performance using revision time & class attendance is a multiple linear regression example.

The variation in performance is explainable using revision time & class attendance. Each variable’s contribution to performance (relative contribution) can be determined.

Let’s discuss simple regression vs multiple regression.

**Simple Regression vs Multiple Regression**

Simple regression uses one independent variable to predict one dependent variable.

Multiple regression predicts one dependent variable using 2/more independent variables.

When predicting exam performance using revision time alone, that’s simple regression.

When predicting exam performance using revision time & class attendance, that’s multiple regression.

**Multiple vs Multivariate Regression**

Multiple regression predicts one dependent variable using 2/more independent variables.

Multivariate regression predicts many dependent variables using one independent variable.

E.g., predicting an individual’s blood pressure & weight using ounces of meat taken.

A *multivariate multiple regression *uses 2/more predictor variables.

E.g., predicting weight & cholesterol using meat (ounces) & chocolate that’s eaten weekly.

**Multiple Regression Analysis with Categorical Independent Variables**

A categorical variable’s values can be grouped via a factor.

Categorical variables should be handled specially in regression analysis because they can’t be entered into a regression equation as they are.

Instead, record them into a series of variables, then feed them into your model.

E.g., predicting income using Education (4 categories) and Age (5 categories).

**What is Multiple Regression Model?**

Although simple regression’s useful, it has limitations.

It can’t match non-linear data.

Its predictions must fit within the range of your training dataset.

Hence, the need for a multiple regression model.

A multiple regression model uses similar logic as a linear regression model.

In simple regression, the observed values of the dependent variable are predicted using a linear function of the observed values of an independent variable.

A multiple regression model predicts the value of a target variable using the linear function of observed values of two or more independent variables.

**Why is Regression Analysis Important****?**

Today, most businesses are defined by data.

Multiple regression can help your business process its data and make better current and future decisions.

Multiple regression’s a good forecasting tool and it can help businesses predict sales and know inventory levels.

Companies can use multiple regression to draw explanations to happenings. For example, why calls from customers have reduced, why one marketing strategy is doing better than the other, etc.

**Common Misconceptions/Mistakes/Myths of Multiple Regression Analysis**

The following are the common myths, misconceptions, and mistakes about multiple regression analysis:

#### 1. Correlation vs Causation

When using multiple regression to explain the impact of some factors on another, always remember that “correlation isn’t causation”.

Consider these two statements:

*“There’s a correlation between rain & sales.”*

*“Sales were caused by rain.”*

The two statements are completely different.

So, factors may be correlated but not connected through cause & effect.

Hence, don’t make assumptions after seeing correlations in regression analysis.

You’ve to step out into the world and establish what’s behind the relationship.

The goal isn’t to know what’s happening in your data but what’s going in the real world.

#### 2. Using Multiple Regression on unclean data

Analyses are sensitive to unclean data.

So, consider the data to gather and how it’s collected to know whether it can be trusted.

It’s hard to get perfect data, but consider doing something during analysis.

You can use “leaky” data if the decisions you need to make have a slight impact on the business.

However, if the decisions may have a huge impact on the business, especially in terms of cost, correct the “leaky” data.

Consider the benefits of taking action against the costs of being wrong.

Regression analysis beginners ignore errors, which is a huge mistake.

It’s dangerous because you make relationships between variables more certain than they’re.

If your mlr model explains 90% of the relationships, it’s okay.

However, if it explains 20% of the relationship, then you treat it like it’s 90%, you’re wrong.

The analysis quantifies the certainty of something happening.

#### 3. Replacing Intuition with Data

Always combine your intuition with data.

Do your analysis results match your understanding?

If anything doesn’t make any sense, consider checking whether there’s an error term.

You can consider checking other analyses or consult from more experienced managers.

Always remember to look beyond the results to what’s going on outside the office.

Your analyses should be paired with a study of the real world.

To become the best manager look at both.

#### 4. Delegating critical tasks to data analysts

Don’t allow your data analysts to go to the field and determine the variables impacting what’s to be predicted.

Most analyses fail to go well because managers have failed to narrow their focus on what to find.

You should identify the variables with an impact and direct your data analyst to focus on them.

If you give the data scientist the freedom to choose what to focus on or to find something you don’t have clues about, you deserve the outcome, which is poor analysis.

So, don’t allow your data scientist to focus on anything they find possible.

Doing that means you’ll find non-existing relationships.

#### 5. Not doing something about the independent variables

You must determine whether something can be done to the independent variable under consideration.

Determine the variables that you’ve control over and those you can’t control.

For example, you can’t control the weather and competitor’s promotions, but you can change your promotions and add features.

So, know what you’ll do with the data.

What actions are to be taken?

What decisions are to be made?

**What is a Multiple Regression Analysis used for?**

Multiple regression is a predictive analysis technique that explains the relationship between one dependent variable and multiple independent variables.

Businesses use it to predict future risks and opportunities. For instance, demand analysis predicts the number of items that a customer will probably buy. Insurance providers use multiple regression to determine the credit standing of policyholders and the possible number of claims within a particular period.

Businesses also use multiple regression to optimize the efficiency of their operations. E.g., a statistical model can be created to determine the impact of various ingredients on the shelf life of cakes. This removes the guesswork for improved decision-making.

Multiple regression is key in identifying and correcting errors. For example, a retail store may consider increasing shopping hours and the number of support staff to boost sales. However, multiple regression may show that the generated revenue won’t be enough to support the increased expenses of hiring additional staff and increasing operating hours. Hence, multiple regression will have prevented mistakes that could have occurred.

Multiple regression is also used to extract insights from data. Today, businesses have gathered huge data volumes from many sources. This data is useless without correct analysis. Multiple regression helps companies discover relationships among variables contained in datasets.

**Conclusion:**

This is what you’ve learned in this multiple regression analysis tutorial:

- Multiple regression involves predicting values of one target variable using two or more predictor variables.
- Simple regression involves predicting one target variable using one predictor variable.
- In multivariate regression, there is one predictor variable and two or more target variables.
- Multiple regression is a key decision-making tool in many businesses.

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