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Application of Linear Regression: Distance Measurement via Ultrasonic Sensor

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Application of Linear Regression: Distance Measurement via Ultrasonic Sensor

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http://pubs.sciepub.com/automation/3/3/6/

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Summarized and Detailed Notes for Week 12 Tutorial

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Summarized and Detailed Notes for Week 12 Tutorial

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Analyzing a Teleport spell

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Analyzing a Fireball spell

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There are several non-linear curves that can be transformed into linear curves. Using a non-linear transformation, you can easily solve non-linear problems as a linear (straight-line) problem.

The following website explains some of the more commonly used non-linear regression models and how to transform them into linear regression:

http://people.revoledu.com/kardi//tutorial/Regression/nonlinear/NonLinearTransformation.htm

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Advanced Application of Linear Regression: Estimating the price of a real estate based on two dependent variables (i.e. 3D data points)

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Advanced Application of Linear Regression: Estimating the price of a real estate based on two dependent variables (i.e. 3D data points)

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Application of Linear Regression: Estimating the price of a real estate

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Application of Linear Regression: Estimating the price of a real estate

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Correlation measures the extent to which two variables have a linear relationship with each other:

https://en.wikipedia.org/wiki/Correlation_and_dependence

It is important to note that Correlation does not imply causation

https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation

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Regression Line minimizes Sum of Squared Error

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Regression Line minimizes Sum of Squared Error

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The Regression Line (in the attached image) is denoted denoted by:
Y = β₀ + β₁ * X

The Sum of Squared Error (in the attached image) is denoted by:
SS(Error) = Σ(yᵢ - Yᵢ)²

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The attached image uses the following notations:

Regression Line is denoted by:
ŷ = β₀ + β₁ * x

Sum of Squared Error is denoted by:
SSE = Σ(yᵢ - ŷᵢ)²

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Regression Line minimizes variance along the y-axis

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Regression Line minimizes variance along the y-axis

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The Regression Line (in the attached image) is denoted by:
E[Y] = β₀ + β₁ * x

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Scatter Plots and More

http://www.regentsprep.org/regents/math/algebra/AD4/PracPlot.htm

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Proof that the regression equation minimizes the squared error to the regression line

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Proof that the regression equation minimizes the squared error to the regression line

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Squared error of regression line

https://www.youtube.com/watch?v=6OvhLPS7rj4

Part 1 of Proof

https://www.youtube.com/watch?v=mIx2Oj5y9Q8

Part 2 of Proof

https://www.youtube.com/watch?v=f6OnoxctvUk

Part 3 of Proof

https://www.youtube.com/watch?v=u1HhUB3NP8g

Part 4 of Proof

https://www.youtube.com/watch?v=8RSTQl0bQuw

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https://padlet.com/mmuvictor/DPS5018_main

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Trim 3, 2015/2016

Q5a

Trim 2, 2015/2016

Section A:

Q20

Section B:

Q1b, Q2b

Trim 2, 2014/2015

Section B:

Q4

Section C:

Q3c

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7.1a) Introduction to Bivariate Data

http://onlinestatbook.com/2/describing_bivariate_data/introM.html

7.1b) Values of the Pearson Correlation

http://onlinestatbook.com/2/describing_bivariate_data/pearsonM.html

7.1c) Properties of r

http://onlinestatbook.com/2/describing_bivariate_data/propertiesM.html

7.1d) Computing r

http://onlinestatbook.com/2/describing_bivariate_data/calculationM.html

7.2a) Introduction to Linear Regression

http://onlinestatbook.com/2/regression/introM.html

7.2b) Regression line example

https://www.youtube.com/watch?v=GAmzwIkGFgE

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Application of Linear Regression: Determining if there is any relationship
between regularly attending classes 
and getting better quiz marks

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Application of Linear Regression: Determining if there is any relationship
between regularly attending classes 
and getting better quiz marks

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Attached are your Quiz 1 marks during the end of Week 4 (i.e. your first attempt at Quiz 1 in MMLS).

After analyzing your Quiz 1 performance using techniques in Topic 7 and Topic 8, I have verified the following facts:

watching the EDpuzzle videos does have a positive affect on your Quiz 1 marks

there is a positive correlation between regularly attending classes and getting better marks in Quiz 1

P.S. If you would like to check out my analysis, you have to download the attached file first :)

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final 1415.pdf

Section A:

Q10

Section C:

Q3c

final 1516.pdf

Section A:

Q19, Q20

Section C:

Q1b, Q2c

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Application of Linear Regression in Machine Learning: predict a quantitative Y based on several (quantitative) X

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Application of Linear Regression in Machine Learning: predict a quantitative Y based on several (quantitative) X

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https://www.ismll.uni-hildesheim.de/lehre/ml-07w/skript/ml-2up-01-linearregression.pdf

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Post good learning materials over here to get your Bonus Marks :)

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These are what you need to know about Topic 7

Correlation and regression

7.1) Linear correlation

7.2) Simple Linear Regression Model