Back To Course

Introduction to Statistics: Homework Help Resource8 chapters | 108 lessons

Watch short & fun videos
**
Start Your Free Trial Today
**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Cathryn Jackson*

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Simple linear regression is a great way to make observations and interpret data. In this lesson, you will learn to find the regression line of a set of data using a ruler and a graphing calculator.

Hannah is a scientist studying the time management and study skills of college students. She conducts an experiment at a local college with 50 students. She asks each student to track their time spent on social media, time spent studying, time spent sleeping and time spent working over the course of a semester. She also asks the students to record their final GPA for the semester.

In this lesson, you will be learning about the simple linear regression and how to find a regression line using a graphing calculator. A **regression line** is a straight line that attempts to predict the relationship between two points, also known as a trend line or line of best fit. **Simple linear regression** is a prediction when a variable (*y*) is dependent on a second variable (*x*) based on the regression equation of a given set of data. We'll see how Hannah uses simple linear regression to help interpret her data.

Once all 50 students turn in their data, Hannah creates a **scatterplot**, which is a graph of ordered pairs showing a relationship between two sets of data. For her first scatterplot, Hannah uses two variables: time spent on social networking and amount of sleep. To simplify her information, we are going to look at the average time per week each student spent sleeping and on social media. Take a look at the scatterplot:

Since we are using two variables, we can call this bivariate data. **Bivariate data** is two sets of variables that can change and are compared to find relationships. Bivariate data is most often displayed visually using a scatterplot.

You may notice that this data has several points that create a sort of pattern. Many of the points increase in the *x* value as they decrease in the *y* value. This is a relationship between the two sets of data known as a **correlation**. A correlation is the relationship between two sets of variables used to describe or predict information.

A regression line is one way of predicting this information and finding a correlation in the data. There are two ways you can find the regression line of a set of data. The first way is to find the regression line by using a ruler, and the second way is to use a graphing calculator. Let's talk briefly about how to find a regression line by hand before we use a calculator.

To find a regression line by hand, follow these steps:

- Draw a line that is closest to as many points as possible.
- Choose two points, and calculate slope.
- Write the equation of the line.

Let's use the scatterplot above to practice finding the regression line using a ruler.

First, use the ruler to find a place that is closest to as many points as possible. Sometimes you can find two points to use.

Second, pick two points you think would be on the regression line. You can use points that are on the line or you can make up new points. Use these points and plug them into the following equation:

If you are unfamiliar with using this equation, check out our algebra lessons!

Third, now you have the slope of your line. You can create an equation based on this information. Find the *y*-intercept by extending the line all the way to the *y*-axis.

Use the slope-intercept equation to create the equation for your line like this:

*y*=*mx*+*b**y*= -1*x*+ 66

Now that you know how to find a regression line by hand, let's talk about how to find a regression line using a calculator. Every calculator is a little bit different. However, you should be able to get by with just about any graphing calculator using these steps:

- Set the calculator to Statistics mode.
- Enter the data (1st Set on L1, 2nd Set on L2).
- Adjust settings for a scatterplot, and then graph the points.
- Set the calculator for regression line.

We will use the data that Hannah collected about the amount of sleep and the amount of work the students did during the semester:

This data is a weekly average for each student. To save time, I'm only using 20 students, rather than the original 50. In this example, I am using a TI-83 graphing calculator.

First, set your calculator to statistics by pressing the Stat button. This will take you to a screen with the options of Edit, Calc and Tests. Select the Edit option by pressing enter. The L1 is the *x*-coordinates, and the L2 is for the *y*-coordinates. Enter each of the coordinates using the number pad and hitting 'Enter' when you are done entering each coordinate. After hitting the enter button, the calculator will take you to the next line for the second coordinate. You can also use the arrow buttons to move between L1 and L2.

Next, adjust the settings on your calculator to display a scatterplot. To do this, hit the 2nd button then hit Statplot. You should see this screen:

Hit Enter to go into the next screen, which looks like this:

Make sure your settings match mine by moving the cursor around with the arrow buttons and selecting each item with the Enter button. Selected items will have a black background and light text.

You will also want to make sure you can see all of your points. I've adjusted the values in each field using the arrow keys, the enter button and the number pad. Push the Graph key to see the points plotted on the graph. Now you are ready to find the equation of your regression line.

First, press the STAT button again. This time, use the arrow keys to move to the CALC option at the top of the screen. Using the arrow keys, move your cursor down to item number four labeled LinReg(*ax* + *b*). Press the enter button.

The calculator will show you the same LinReg(*ax* + *b*) at the top of the screen. Hit enter a second time to calculate the regression line.

*a*= 1.3*b*= 40.6

Therefore, the equation for the regression line is *y* = 1.3*x* + 40.6. My graph would look like this:

Now Hannah wants to compare the amount of time a student spends studying to the amount of time the student spends sleeping. Can you find the regression line and its equation from this set of data? Pause the video here to work on this problem.

Sleep Time (Hours) | Study Time (Hours) |
---|---|

70 | 6 |

64 | 4 |

60 | 7 |

57 | 8 |

56 | 6 |

54 | 10 |

52 | 12 |

50 | 10 |

49 | 11 |

47 | 9 |

47 | 8 |

46 | 4 |

50 | 6 |

45 | 7 |

42 | 10 |

40 | 8 |

38 | 9 |

35 | 10 |

49 | 5 |

49 | 4 |

The equation for the regression line on this graph is *y* = -0.0989*x* + 12.643. If you rounded numbers here, that's okay for this problem.

Don't forget to press 'enter' when you see the LinReg(*ax* + *b*) on your calculator. It will not show you the values for *a* and *b* if you don't press enter, telling the calculator to find these variables.

Okay, try this. Hannah now wants to compare the time a student spends studying to his or her GPA. Can you find the regression line and its equation from this set of data? Feel free to pause the video here while you work.

Study Time (Hours) | GPA (Semester) |
---|---|

6 | 2.6 |

4 | 2.2 |

7 | 2.9 |

8 | 3.4 |

3 | 3.5 |

10 | 4 |

12 | 4 |

10 | 3.8 |

11 | 3.6 |

9 | 4 |

8 | 3.7 |

4 | 4 |

6 | 2.4 |

7 | 3.5 |

10 | 3.2 |

8 | 3.3 |

9 | 3.9 |

10 | 3.7 |

5 | 2.6 |

4 | 2.3 |

The equation for the regression line on this graph is *y* = .1683 + 2.0343. If you rounded numbers here, that's okay for this problem. If you did not get the correct answer here, feel free to go back in the video and follow the steps again with me.

In summary, a **regression line**, also known as a trend line or line of best fit, is a straight line that attempts to predict the relationship between two points. **Simple linear regression** is a prediction when a variable (*y*) is dependent on a second variable (*x*) based on the regression equation of a given set of data.

Every calculator is a little bit different. However, you should be able to get by with just about any graphing calculator using these steps:

- Set the calculator to Statistics mode.
- Enter the data (1st Set on L1, 2nd Set on L2).
- Adjust settings for a scatterplot, and graph the points.
- Set the calculator for regression line.

Finally, if you get any errors or the information doesn't look correct, double check the points you entered first, and then review the settings on the calculator.

Watch this video lesson, then see how well you can:

- Provide definitions for 'regression line' and 'simple linear regression'
- Create a scatterplot
- Present a step-by-step method for using a graphing calculator
- Find the regression line of a set of data using a ruler and a graphing calculator

To unlock this lesson you must be a Study.com Member.

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
2 in chapter 8 of the course:

Back To Course

Introduction to Statistics: Homework Help Resource8 chapters | 108 lessons

- Creating & Interpreting Scatterplots: Process & Examples 6:14
- Simple Linear Regression: Definition, Formula & Examples 9:52
- Analyzing Residuals: Process & Examples 5:30
- Interpreting the Slope & Intercept of a Linear Model 8:05
- The Correlation Coefficient: Definition, Formula & Example 9:57
- How to Interpret Correlations in Research Results 14:31
- Correlation vs. Causation: Differences & Definition 7:27
- Interpreting Linear Relationships Using Data: Practice Problems 6:15
- Transforming Nonlinear Data: Steps & Examples 9:25
- Coefficient of Determination: Definition, Formula & Example 5:21
- Go to Regression & Correlation: Homework Help

- Influence & Persuasion for Front-Line Managers
- Purpose-Driven Business Leadership
- Lean-Agile Mindset for Leaders
- Reducing Stress for Supervisors
- Team Building Skills for Supervisors
- Designing Influential Messages in Business
- Aligning Jobs, Goals, Purpose & Agenda
- Continuous Lean Process Improvement
- Overcoming Obstacles to Influence & Persuasion in Business
- Techniques & Tools for Influence in Business
- CLEP Exam Question Formats
- CLEP Exam Costs & Registration Deadlines
- CLEP Exam List & Credits Offered
- How to Request a CLEP Transcript
- CLEP Exam Dates & Testing Center Locations
- CLEP Scoring System: Passing Scores & Raw vs. Scaled Score
- Continuing Education Opportunities for Molecular Biology Technologists

- Human Resources Management for Hospitality
- Willowbrook Hepatitis Experiments: Bioethics Case Study
- The Full Cycle of Event Planning in a Hotel
- The Electrical Stimulation Method: Theorists, Research & Applications
- Higher-order Determinants Lesson Plan
- Using Anecdotes to Persuade an Audience
- What Are Civil Disturbance Operations?
- Value Creation in Business: Definition & Example
- Quiz & Worksheet - Angles in Standard Position
- Quiz & Worksheet - Sustainable Tourism
- Quiz & Worksheet - Rhetorical Devices in In Cold Blood
- Quiz & Worksheet - Personalistic & Naturalistic Theory in Science
- Quiz & Worksheet - Synopsis of Wonder by R.J. Palacio
- Tourism Marketing Flashcards
- Tourism Economics Flashcards

- Tips for First-Time Managers
- NY Regents Exam - Chemistry: Test Prep & Practice
- SAT Math Prep: Review & Practice
- Strategic Management in Business
- American Revolution Study Guide
- SAT Subject Test Literature: Authors & Works from English Literature
- Antimicrobial Drugs: Tutoring Solution
- Quiz & Worksheet - Executive, Legislative & Judicial Branches of Government
- Quiz & Worksheet - The Picornaviridae Virus Family
- Quiz & Worksheet - Determining Venue for a Court Case
- Quiz & Worksheet - Taking Questions in a Business Presentation
- Quiz & Worksheet - Rights of Promisors and Promisees in Contracts

- Emotions in the Workplace: Purpose & Functions
- Do Humans Have an Open or Closed Circulatory System?
- Scholarships for Homeschoolers
- Middle Ages Lesson Plan
- How to Get Tuition Reimbursement
- Enlightenment Lesson Plan
- Narrative Writing Lesson Plan
- Arizona Science Standards
- Haitian Revolution Lesson Plan
- Creative Writing Prompts for Middle School
- Homeschooling in Alabama
- The Raven Lesson Plan

Browse by subject