Brock University Line of Best Fit Questions

User Generated

rinalh

Mathematics

Brock University

Description

Your friend is taking an introductory statistics course and is now learning about linear regression. They are having a difficult time understanding how scatterplots, line-of-best-fit, Pearson’s r, residuals, squared residuals, outliers and R-squared relate to each other. Your friend says they are a “visual learner” and gets confused by all the calculations and R code. They think if only they could understand the big picture, maybe they would understand what each calculation and R command does.   

While thinking of how to help your friend, you stumble across this website:
(link: https://phet.colorado.edu/sims/html/least-squares-regression/latest/least-squares-regression_en.html ). This URL leads to a web application that allows you to create and calculate a scatterplot, a line-of-best-fit, residuals, squared residuals and Pearson’s r. It also shows you the regression equation. Best of all, this application operates in real time and lets you create custom scatterplots.

Prompt

Design three to seven screenshots and supporting text that allow you to demonstrate the following to your friend: 

1. How the line of best-fit changes as new observations are added or removed.
2. How outliers can impact the strength and direction of Pearson’s r.  
3. How Pearson’s r changes as new observations are added or removed.  
4. How the residuals (AKA error terms or deviations) change as new observations are added or removed.
5. How better fitting lines produce smaller squared residuals.  
6. How better fitting lines produce higher values of Pearson’s r.  
7. How Pearson’s r (and R-squared, a measure of goodness-of-fit) is independent of the slope of the line.

Unformatted Attachment Preview

Objective 1. Develop and demonstrate intuition about the relation between line-of-best-fit and Pearson's r measure of linear association; 2. Develop and demonstrate intuition about the relation between line-of-best-fit and residuals; 3. Develop and demonstrate intuition about the relation between line-of-best-fit and squared residuals; 4. Develop and demonstrate intuition about the relation between line-of-best-fit and outliers; and 5. Develop and demonstrate intuition about the relation between Pearson's r and R-squared. 6. Develop your visual presentation skills. Instructions Scenario Your friend is taking an introductory statistics course and is now learning about linear regression. They are having a difficult time understanding how scatterplots, line-of-best-fit, Pearson's r, residuals, squared residuals, outliers and R-squared relate to each other. Your friend says they are a “visual learner" and gets confused by all the calculations and R code. They think if only they could understand the big picture, maybe they would understand what each calculation and R command does. While thinking of how to help your friend, you stumble across this website: (link: https://phet.colorado.edu/sims/html/least-squares-regression/latest/least-squares-regression_en.html). This URL leads to a web application that allows you to create and calculate a scatterplot, a line-of-best-fit, residuals, squared residuals and Pearson's r. It also shows you the regression equation. Best of all, this application operates in real time and lets you create custom scatterplots. Prompt Design three to seven screenshots and supporting text that allow you to demonstrate the following to your friend: 1. How the line of best-fit changes as new observations are added or removed. 2. How outliers can impact the strength and direction of Pearson's r. 3. How Pearson's r changes as new observations are added or removed. 4. How the residuals (AKA error terms or deviations) change as new observations are added or removed. 5. How better fitting lines produce smaller squared residuals. 6. How better fitting lines produce higher values of Pearson's r. 7. How Pearson's r (and R-squared, a measure of goodness-of-fit) is independent of the slope of the line. Remember to provide sufficient explanatory text --- but not too much --- as you do this. Use a roughly linear pattern in your scatterplot and trim your screenshots of extraneous material.
Purchase answer to see full attachment
Explanation & Answer:
7 Questions
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer

Attached.

1
-

1. The line of best-fit changes with new observation depending on the values added, for
instance where an observation has a higher value of y, the gradient and constant tend to
increase the two figures below show the change in the line of best fit.

The added observation is shown on the second image.

2
-

-

-

2. Ou...


Anonymous
Really helped me to better understand my coursework. Super recommended.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4
Similar Content
Related Tags