Difference between revisions of "Least squares modelling"
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* Run the code below to see how to build and use a linear model in R, but see [[Software_tutorial | step 16 and onwards]] in the R tutorial as well. | * Run the code below to see how to build and use a linear model in R, but see [[Software_tutorial | step 16 and onwards]] in the R tutorial as well. | ||
* Try some [[Practice_questions|practice problems]]. | * Try some [[Practice_questions|practice problems]]. | ||
* Describe a linear regression model you have made for a lab report. | |||
** What was the $$R^2$$ value? | |||
** How did you calculate the regression model values? | |||
** Use the same data from your report and instead calculate the standard error, $$S_E$$. How do you interpret that $$S_E$$ value now? | |||
* Do the YouTube challenge: find a video on YouTube that explains the central limit theorem, or the confidence interval, or least squares in a way that is different to explained in class (hopefully you find better explanations than mine). Share the link with a friend in your class. | |||
* [http://www.nejm.org/doi/full/10.1056/NEJMon1211064 Does eating chocolate lead to winning a Nobel prize]? | * [http://www.nejm.org/doi/full/10.1056/NEJMon1211064 Does eating chocolate lead to winning a Nobel prize]? | ||
== Resources == | |||
<!-- | |||
* [[Image:Nuvola_mimetypes_pdf.png|20px|link=Media:2015-4C3-6C3-Least-squares-modelling.pdf]] [[Media:2015-4C3-6C3-Least-squares-modelling.pdf| Class notes 2015]] | |||
* [[Image:Nuvola_mimetypes_pdf.png|20px|link=Media:2014-4C3-6C3-Least-squares-modelling.pdf]] [[Media:2014-4C3-6C3-Least-squares-modelling.pdf | Class notes 2014]] | |||
* [http://learnche.org/pid/least-squares-modelling/index Textbook, chapter 4] | |||
* Quizzes (with solutions): attempt these after you have watched the videos | |||
:{| class="wikitable" | |||
|- | |||
! Tasks to do first | |||
! Quiz | |||
! Solution | |||
|- | |||
| Complete steps 10, 11, 12 and 13 of the [http://learnche.mcmaster.ca/4C3/Software_tutorial software tutorial] | |||
(also steps 1 through 9) | |||
| [ Quiz] | |||
| [ Solution] | |||
|- | |||
| Watch videos 1, 2, 3, 4, and 5 | |||
| [https://docs.google.com/document/d/19NnM1v7yut1q0HFaHMQmNg6zMH2UPN1rrHZl7l38qBI Quiz] | |||
| [https://docs.google.com/document/d/1YcF4PxxfQqnz4UqgGZMWv3zfFmmjB7uSkNfQ9XMe97A Solution] | |||
|- | |||
| Watch videos 6, 7, and 8 | |||
| [https://docs.google.com/document/d/1BySja0o1O8MtZOitV42BU2bnjWmzH_vARcXCbh5OviI Quiz] | |||
| [https://docs.google.com/document/d/17jKKHwgVLkBT04R3OgUr9TqSzCGkxVYBP-fZtuiszig Solution] | |||
|- | |||
| Watch videos 9 and 10 | |||
| [https://docs.google.com/document/d/1qMBqum4kdgLBK3dlzXncZJm42NKdp8pnsp9jxG_dKXA Quiz] | |||
| [https://docs.google.com/document/d/19mCY3qCpVKLzvOBpa-c1t7JDzLTl0xagnivRpslnTD0 Solution] | |||
|- | |||
| Watch videos 11, 12, and 13 | |||
| [https://docs.google.com/document/d/1zxOUn30wTeg8xiJfIgfZ3WKgiUk3hqrnCV-sDTrlFiA Quiz] | |||
| [https://docs.google.com/document/d/19RozNWVpmQo5oJOfw2SDhWZrJ2Sbpq2LuWFq8NsLN6g Solution] | |||
|- | |||
| Watch videos 14, 15, and 16 | |||
| [https://docs.google.com/document/d/1ZJ1aZ-hvS11-k5btkBqb1X16RAihbFTDjX-fNX8iQm8 Quiz] | |||
| [https://docs.google.com/document/d/10h2qavaw08AYC5qGAWyemXrgro0F-ARBaDnoE52S77Y Solution] | |||
|} | |||
--> | |||
Revision as of 15:31, 3 January 2016
Learning outcomes
- Understand the difference between correlation and covariance.
- What the objective function of least squares does
- Understand and use an analysis of variance table
- Calculate and interpret the confidence intervals from a least squares model
- Know about the assumptions required to interpret least squares model coefficients
- Use the prediction error range from the model
- Identify outlier points and classify them
- Use the linear model when there are multiple predictor variables (this is what we are building up towards; we will use this extensively in the next topic)
Extended readings/practice
- Run the code below to see how to build and use a linear model in R, but see step 16 and onwards in the R tutorial as well.
- Try some practice problems.
- Describe a linear regression model you have made for a lab report.
- What was the $$R^2$$ value?
- How did you calculate the regression model values?
- Use the same data from your report and instead calculate the standard error, $$S_E$$. How do you interpret that $$S_E$$ value now?
- Do the YouTube challenge: find a video on YouTube that explains the central limit theorem, or the confidence interval, or least squares in a way that is different to explained in class (hopefully you find better explanations than mine). Share the link with a friend in your class.
- Does eating chocolate lead to winning a Nobel prize?