In our writing, as an industrial engineering student, I’d like to mention how to do a scientific **forecast**. In this writing we will talk about questions like what is, when and for which purposes to do “Regression Analysis”, **as well as** see how to mathematically arrive a conclusion.

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## What is Mathematical Prediction Regression Analysis?

We can say that regression analysis is, in basic, a relationship between two variables. But how do we establish this relationship?

Generally, for every prediction we will make for the future we use experiences that we acquire in the past. Cloudy weather can help you predict whether it will rain or not because of the data you use from past to future and its cause and effect relationship.

These cause and effect relationships include the weakening of the grades of a student who is absent in education; For a business, we can observe it as an increase in sales as a result of more social media ads.

## What is the Objective of Regression Analysis, When is it Done?

Like we said, regression analysis consists of predictions about future by using the past.

Think about you have a pizza store and you sell pizzas. How do you guess what kind of people would buy pizza or what kind of people order which kind of pizza? In here, the most basic thing to do would be paying attention to properties like ages, heights, financial positions etc. of people who ordered the same kind of pizza. Because aside from these you do not know anything about the other person. You have no idea about what they think, what flavors or tastes they have. Then we will fully use similarities between the **orderers**.

**For a change**, let’s think about we are mobile ice cream seller. We are selling ice cream in a park. If 50 people bought ice cream from us today, then how do we guess how many people will buy in the same day a year later? For this we, again, will use similar parameters. We can mathematically do this guess by taking account of parameters like how many people bought which ice cream, exactly where did we sell ice cream, which days did we sell, what was the temperature of the air and were there anyone else who has similar sales. Since we have to possess lots of data for this guess, we have to repeat this until the same day next year, so we get a lot of data and come up with more realistic outcomes.

## Mathematical Definition of Regression Analysis

Regression Analysis is viewed by two ways.

Simple regression analysis

Multivariable regression analysis

__Simple regression analysis:__ Y = a + bX + u

__Multivariable regression analysis:__ Y = a + b1X1+ b2X2+ b3X3+…+ u

Identified like this. In calculating this formula “b” became our cause while “Y” become our outcome.

Aside from this formula extra formulas are used for calculating a and b. These are;

Given like this. Here, a calculation is made **within** the information you will obtain from the table and a result is reached for a value you want.

This technique is generally used to assist in finance and investment. Data we have and outcomes we obtained bring us closer to the rational by using cause and effect between variables.

## Useful Vocabulary

**Forecast (n):** a statement about what will happen in the future, based on information that is available now

**As well as (something) (idiom):** in addition to somebody/something

**Orderer (n):** Someone who make requests for food or drinks in a restaurant, bar, etc.

**For a change (idiom):** as something different from what is usual

**Within (preposition):** inside the range or limits of something