# What Does Regression Analysis Tell You?

What does linear regression tell you?

## What is regression analysis used for?

Regression analysis is most often used for two reasons:

### Making variable predictions

A company or organization may use a regression analysis to forecast a specific dependent variable. By entering data for the independent variables and analyzing their effects on the dependent variable, a business achieves this.

For instance, if a business wanted to forecast its projected sales income for the quarter (the dependent variable), it could use a regression analysis to estimate it by filling in the specifics for the number of salespeople it employs, the number of days in its sales quarter, and the price of its services (the independent variables).

### Estimating a variable effect

Regression analysis can also be used to calculate the potential impact of a single independent variable on the results of a dependent variable. You can run a regression analysis to test the theory, for instance, if a coworker claims that a company’s outdated website (the independent variable) directly affects the company’s sales.

Regression analysis can help you confidently identify and resolve issues a company is having, as well as enhance its goods and services. Predicting variables and estimating their effects

## What is regression analysis?

A statistical method for examining the relationship between two or more relevant variables is regression analysis. It can benefit a business or company in a variety of ways and has a variety of variations depending on its intended use and the number of variables present.

## How does regression analysis work?

Regression analysis evaluates the relationship between one dependent variable and one or more independent variables by assigning values to both. For instance, if you believe that a book will sell more copies if it has an attractive cover, you could use regression analysis to see if there is a relationship between those two variables:

### 1. Create two sets of data

Making two sets of data is the first step in analyzing the relationship between the quantity of books sold (the dependent variable) and how attractive their covers were (the independent variable). Take a random selection of books for the first set of data, and note how many copies were sold when each was published.

After that, ask the purchasers of each book in your first set of data one simple question: “Do you like the cover?” In order to study the regression analysis, the answers to this question should result in the second set of data.

### 2. Graph them

You can graph the results more easily for this study because there are only two sets of data and one independent variable to be examined. The number of books sold on the graph’s y-axis can be considered the dependent variable, and the number of buyers who liked the book covers on the x-axis can be considered the independent variable. Combine the data sets after that, and then use the appropriate axes to graph the results.

### 3. Find any correlations

You might start to notice some correlations in the data once you’ve graphed your variables. For instance, you might see an upward slope suggesting a positive relationship between the number of books sold and how well-liked the covers were, or you might see a downward slope suggesting a negative relationship between a fancy cover and the number of books sold.

The data could, however, be so arbitrary that there is no correlation at all. If this is the case, you might think about gathering additional data to see if your findings change or you might think about completely changing your hypothesis.

### 4. Find your regression line

Consider drawing a line through the center of your data if you’re having trouble seeing a correlation or want to further investigate it after you’ve graphed your data. In addition to physically drawing this with a straight edge and your best guess, you can also use mathematical software to create a more precise graph and line through the center.

The regression line is this line, and it can be used to show how your variables are related. If you’re using a mathematical program, the regression line can also give you a precise formula that will allow you to calculate and forecast various variables in the future. The regression line can assist you in understanding the positive or negative direction of the data.

## Regression analysis variations

Here are a few examples of different regression analysis variations:

### Simple Linear

Y = a + bX + ∈

One dependent variable and one independent variable are used in simple linear regression analysis. A simple linear regression analysis would be used to answer the question, “Do attractive book covers increase book sales?”

The variables of this equation are:

Because independent variables cannot accurately predict the outcome of dependent variables, there is always an error term included in the calculation of a regression line and any regression analysis.

### Multiple linear

Y = a + b X1 X 2 X 3 +

Regression analysis with multiple independent variables but one dependent variable is known as multiple linear. For instance, building on the prior hypotheses of book sales, if you believe that book titles and book size also influence how many copies sell, you can include those as independent variables in a multiple linear regression analysis along with book covers.

The variables in this equation are:

When using a multiple linear regression analysis, the independent variables’ correlations with the dependent variable and regression lines’ slopes must differ. Otherwise, the graph might become too complex to understand if each regression line is similar to the next.

### Nonlinear

Using dependent and independent variables whose relationships are difficult for a normal linear regression line to define, a nonlinear form of regression analysis is used. Nonlinear regression analysis employs more complex data sets, and its regression line is frequently curved to better reflect the relationship between the variables.