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# What do the Coefficients of a Regression Model Indicate?

“Correlation does not (necessarily) imply causation,” you must have heard this famous sentence in case you took an introductory inferential statistics/data science class. At the same time, as you carefully explore academic/non-academic research, you realize that perhaps in all cases, the first step in inferring a causal relationship between a predictor and an outcome is to find the existence of correlation/association between them.

For example, based on the evidence of a lower number of COVID-19 cases in warmer places than in colder places, some researchers suggest that coronavirus transmission becomes slower with the increase in temperature. Essentially, researchers found a negative correlation between the increase in temperature and in COVID-19 cases, and postulated (with caution) a causal relationship. So, correlation can imply causation, huh!

In case you build regression models for your academic/non-academic research, you must also know that the coefficient of a predictor in a regression model expresses the correlation/association between the predictor and an outcome. In this article, we will try to understand under what circumstances the coefficient of a predictor can also (potentially) indicate the causal effect of the predictor on an outcome. Using an example with three scenarios, we are going to shed light on the correlation-causation conundrum.

Example

A restaurant business analyst is trying to investigate the causal relationship between sending discount cards to home addresses and the monthly count of customer visits to a restaurant.

Scenario 1: A Simple Linear Regression Model Using Non-Experimental Data

The analyst finds a dataset that includes data on whether restaurants sent discount cards and on the count of customer visits to restaurants during the month of X for all the restaurants in the city of Y.

Next, based on the data, the analyst builds the following regression model in which Discount Card Sent is a binary predictor (1=Yes, 0=No) and Monthly Count of Customer Visits is a continuous outcome:

Monthly Count of Customer Visits = 1951 + 674 * Discount Card Sent

Based on the above model, if a restaurant sends discount cards, the expected Monthly Count of Customer Visits = 1951+674*1 = 2625

And, if a restaurant does not send discount cards, the expected Monthly Count of Customer Visits = 1951+674*0 = 1951

The analyst concludes: compared against the_ restaurants that do not send discount cards_, the _restaurants that send discount _cards, on average, get 2625–1951 = 674 more customer visits per month.

Apparently, sending discount cards to home addresses can induce more customer visits to a restaurant as discount cards make food items more affordable. But, based only on the results of the bivariate analysis (linear regression model with only one predictor), can the analyst suggest that in the next month, restaurants that will send discount cards will, on average, get more customer visits than restaurants that will not send discount cards?

#machine-learning #causality #data-science #data analysis

## Buddha Community  1598352300

## Regression: Linear Regression

Machine learning algorithms are not your regular algorithms that we may be used to because they are often described by a combination of some complex statistics and mathematics. Since it is very important to understand the background of any algorithm you want to implement, this could pose a challenge to people with a non-mathematical background as the maths can sap your motivation by slowing you down. In this article, we would be discussing linear and logistic regression and some regression techniques assuming we all have heard or even learnt about the Linear model in Mathematics class at high school. Hopefully, at the end of the article, the concept would be clearer.

**Regression Analysis **is a statistical process for estimating the relationships between the dependent variables (say Y) and one or more independent variables or predictors (X). It explains the changes in the dependent variables with respect to changes in select predictors. Some major uses for regression analysis are in determining the strength of predictors, forecasting an effect, and trend forecasting. It finds the significant relationship between variables and the impact of predictors on dependent variables. In regression, we fit a curve/line (regression/best fit line) to the data points, such that the differences between the distances of data points from the curve/line are minimized.

#regression #machine-learning #beginner #logistic-regression #linear-regression #deep learning 1592023980

## 5 Regression algorithms: Explanation & Implementation in Python

Take your current understanding and skills on machine learning algorithms to the next level with this article. What is regression analysis in simple words? How is it applied in practice for real-world problems? And what is the possible snippet of codes in Python you can use for implementation regression algorithms for various objectives? Let’s forget about boring learning stuff and talk about science and the way it works.

#linear-regression-python #linear-regression #multivariate-regression #regression #python-programming 1601431200

## Polynomial Regression — The “curves” of a linear model

The most glamorous part of a data analytics project/report is, as many would agree, the one where the Machine Learning algorithms do their magic using the data. However, one of the most overlooked part of the process is the preprocessing of data.

A lot more significant effort is put into preparing the data to fit a model on rather than tuning the model to fit the data better. One such preprocessing technique that we intend to disentangle is Polynomial Regression.

#data-science #machine-learning #polynomial-regression #regression #linear-regression 1603170000

## Diagnose the Generalized Linear Models

Generalized Linear Model (GLM) is popular because it can deal with a wide range of data with different response variable types (such as binomial_, Poisson, or _multinomial).Comparing to the non-linear models, such as the neural networks or tree-based models, the linear models may not be that powerful in terms of prediction. But the easiness in interpretation makes it still attractive, especially when we need to understand how each of the predictors is influencing the outcome.The shortcomings of GLM are as obvious as its advantages. The linear relationship may not always hold and it is really sensitive to outliers. Therefore, it’s not wise to fit a GLM without diagnosing.In this post, I am going to briefly talk about how to diagnose a generalized linear model. The implementation will be shown in R codes.There are mainly two types of diagnostic methods. One is outliers detection, and the other one is model assumptions checking.

### Residuals

Before diving into the diagnoses, we need to be familiar with several types of residuals because we will use them throughout the post. In the Gaussian linear model, the concept of residual is very straight forward which basically describes the difference between the predicted value (by the fitted model) and the data. Response residuals

In the GLM, it is called “response” residuals, which is just a notation to be differentiated from other types of residuals.The variance of the response is no more constant in GLM, which leads us to make some modifications to the residuals.If we rescale the response residual by the standard error of the estimates, it becomes the Pearson residual.

#data-science #linear-models #model #regression #r 1598811480

## Modelling Multiple Linear Regression Using R (research-oriented modelling

### Article Outline

• Dataset description
• Exploratory data analysis
• A simple linear regression model fitting
• Model interpretation
• MLR regression model fitting and interpretation
• Hypothesis testing
• Stepwise regression

### Aim

The aim of this article to illustrate how to fit a multiple linear regression model in the R statistical programming language and interpret the coefficients. Here, we are going to use the Salary dataset for demonstration.

### Dataset Description

The 2008–09 nine-month academic salary for Assistant Professors, Associate Professors and Professors in a college in the U.S. The data were collected as part of the on-going effort of the college’s administration to monitor salary differences between male and female faculty members .

The data frame includes 397 observations and 6 variables.

rank (I1): a factor with levels AssocProf, AsstProf, Prof

discipline (I2): a factor with levels A (“theoretical” departments) or B (“applied” departments).

yrs.since.phd (I3): years since PhD.

yrs.service (I4): years of service.

sex (I5): a factor with levels Female and Male

salary (D): nine-month salary, in dollars.

Where** I: **Independent variable; D: Dependent/Outcome variable

The first step is to start installing and loading R libraries

``````## use install.packages( ) function for installation

library(tidyverse)  ## data loading, manipulation and plotting
library(carData)    ## Salary dataset
library(broom)      ## tidy model output
``````

Print dataset details

Let’s print different inbuilt datasets offered by the carData package.

``````data(package = "carData")
`````` #machine-learning #coefficient #stepwise #interpretation #regression