AMU MATH 120 Intro to statistics WEEK 2 lesson NUMERICAL MEASURES, CORRELATION, AND REGRESSION American Military University

**WEEK 2: NUMERICAL MEASURES, CORRELATION, AND REGRESSION****Lesson Overview**

In this lesson we will be studying measures of central tendency, measures of variation, measures of position, correlation and linear regression.**Students will be able to:**- Find measures of central tendency, measures of variation, and measures of position and quantitative data
- Define linear regression
- Interpret the correlation coefficient and the coefficient determination in a linear regression model
- Find the equation of a regression line
- Use the linear regression model to predict the dependent variable
**In this lesson, we will discuss:** - Scatter Plot, Linear Regression and R value
- You will also learn how to find it using Excel.
**Key Learning Concepts** - Explain the use and misuse of statistical concepts.
- Compute measures of central tendency and measures of dispersion to summarize data collected from real world scenarios.
- Explain the relationship between variables with simple linear regression techniques.
**The following activities and assessments need to be completed this week:** - Reading: Understanding Basic Statistics – Chapters 3-4
- Forum 2 – Scatter Plot, Linear Regression and R value
- Homework 2 in WebAssign
- Quiz 1 in WebAssign and complete the critique in the Assignment link

These are some important things to note:

- Finding the measure of central tendency, and position
- Finding the scatter points, r value and linear regression line.

**The readings support the following learning objectives:**

CO-1. Apply fundamental statistical concepts across a variety of disciplines.

CO-2. Apply descriptive statistics techniques to explain data collected from real world scenarios.

CO-3. Apply simple linear regression techniques to understand the relationship between two variables.

Here are the excel instructions for the r value, scatter plot and regression line. Enter the x and the y values into 2 columns in an excel spreadsheet. Here is an example. Put your x in here and your y in here. Put the x values in and then put the y values in. 105 100 125 110 155 160. Let’s do 145. The first thing you do is to cover with the mouse all the values in the x and y columns, so you highlight the values.

Then you go to the insert menu. I’m going to have to move my screen up a little bit where you can see the insert menu. You’ll hit insert. You’ll come over here and you will see in this excel version. It is right here. The scatter plot is right above charts. You click on that and choose this one that looks like this scatter plot. And it is going to put these values into a chart.

The next thing you do is you will click on one of these data points. Right click and you will select add trendline. So, then it is going to put a line along here. And then you are going to click on the line and say format trendline. So, it is a little bit different with each version of excel. And so, it will either pop up a box or you will see this box to the right side. Now I am going to move the screen, so you can see the box to the side. So, we’re going to click on display equation in chart and display r value on chart. So, what that does is it basically gives you these values. I am going to move them up where you can see them.

So this is y=30.87x-30.137. That is your linear regression line. The number in front of the x is the slope and so if that slope is positive then your r value is positive. Now we need to find the r value. We’ve already found the scatter plot. We’ve already found the linear regression line which you can use to work your homework problems. Then with the r squared value we need to find the r value which is just the square root of the r squared value. And you also take the sign of the slope. And this slope is positive because what is in front of the x is positive. So, your r value will be positive.

If what is in front of the x is negative and if this little slope here instead for going up it went down then your r value would be negative and we would put a negative in front of it.

Now to find the r value, just click on any cell. We are going to take the square root of the r squared value. And a quick way to do that is to put =.485 and instead of hitting a square root, we just put ^ .5. Now the caret key is the shift 6. And it puts that little caret ^ .5 and that is the same as the square root. You can do this with a calculator or excel to take a square root. Because it is raising it to the .5 power with is the one half power which is the same as a square root. When you hit enter, it gives you the value. So, if you were rounding then you would have .696. It depends on what they are asking for.

Now I am going to write r= and I’m not going to change this to negative because we know that the slope is positive. We see the slope in the linear regression line that it is in front of the x and we can also see the slope is going upward so it is positive. So now we have the linear regression line. Y=30.86x-30.187. We have the r value, we have the r squared value and we have the scatter plot.

So, you will want to practice this and these instructions are also in the announcements.

**Assignment – Homework 2**

Homework 2 will be completed in WebAssign. WebAssign is interactive and will assist the students in learning the course objectives for the week.

**This assignment corresponds to the following course objectives: **

- Compute measures of central tendency and measures of dispersion to summarize data collected from real world scenarios.
- Apply simple regression techniques to explain the relationship between variables.

**Quiz – Quiz 1 week 2**

**Quiz 1 Week 2** will be completed in WebAssign. WebAssign quizzes will test the students ability to retain the information on the course objectives for the week.

After taking your quiz, go to assignments, Quiz 1 critique and write down what you missed. If you did not miss anything then state that you understood everything or that you made a 100. This will need to be completed before your grade is posted.

**This assessment corresponds to the following course objectives:**

- Explain the use and misuse of statistical concepts..
- Compute measures of central tendency and measures of dispersion to summarize data collected from real world scenarios.
- Explain the relationship between variables with simple linear regression techniques.