Learning Objectives:

__Math Tutoring on Performing Linear Regression__

In statistics **Regression Analysis** involves any technique for modeling and analyzing trends between a **dependent variable**, often **y** and an **independent variable**, often **x**. **Regression analysis** helps us make predictions outside of the given data. If the prediction is within the** range** of the given data, it is called **Interpolation** and if the prediction is outside the range of the given data, it is called **Extrapolation**. When analyzing data, the first step is usually to create a **Scatter Diagram **or** Scatter Plot.** This is just graph using the coordinate plane to display the values of the two variables as a collection of points. It is important to remember to label the **x **and** y axes** to know what they represent. So when we are talking about **linear regression,** there is the term called **Correlation Coefficient**, identified as R or r. The **linear correlation coefficient** measures the strength and direction of the linear relationship between the two variables. The **regression line** or **line of best fit** is graphed over the **scatter plot**. So **R** with a value of positive **1**is a perfect linear fit with a positive slope and the points are tightly clustered along a line. **R** with a negative slope means that **R** would be close to the value of **-1**. If there is no correlation at all, **R** will have a value close to **zero**.

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**Hook Questions:**

*1. **What is the difference between interpolation and extrapolation?*

*2. **What is Correlation Coefficient?*

*3. **Explain the values of r as 1, -1 and 0.*

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