SlideShare a Scribd company logo
Multivariate Linear Regression
More notation
Hypothesis
• hθ(x) = θ0 + θ1x
• hθ(x) = θ0 + θ1x1 + θ2x2 + θ3x3 + θ4x4
• hθ(x) = θ0x0 + θ1x1 + θ2x2 + θ3x3 + θ4x4
Gradient Descent
Gradients
Gradient Descent in
practice: Feature
scaling
• x1 = size (0 - 2000 feet)
• x2 = number of bedrooms
(1-5)
• Divide to max
• Mean norm
Learning Rate α
Make sure gradient descent is working
Features and
polynomial regression
• Often, by defining new
features you may get a
better model
Normal equation
• Normal equation
solves θ analytically

More Related Content

What's hot

Polynomials
PolynomialsPolynomials
Polynomials
SUPER ULTRON
 
Limit - Mohd Noor
Limit - Mohd NoorLimit - Mohd Noor
Limit - Mohd Noor
Mohd. Noor Abdul Hamid
 
Presentacion calculo jan
Presentacion calculo janPresentacion calculo jan
Presentacion calculo jan
jantrevino
 
Programming exercisesn NUMERICAL ANALYSIS
Programming exercisesn NUMERICAL ANALYSISProgramming exercisesn NUMERICAL ANALYSIS
Programming exercisesn NUMERICAL ANALYSIS
Ali Ameer
 
Limit of functions
Limit of functionsLimit of functions
Limit of functions
Juan Apolinario Reyes
 
Fundamental theorem of algebra
Fundamental theorem of algebraFundamental theorem of algebra
Fundamental theorem of algebra
Ramón Zurita
 
The Definite Integral
The Definite IntegralThe Definite Integral
The Definite Integral
Silvius
 
Application of derivatives
Application of derivativesApplication of derivatives
Application of derivatives
Parag Parekh & Co. Chartered Accountants
 
Polynomials
PolynomialsPolynomials
Polynomials
Ankit Goel
 
Lesson 7: Limits at Infinity
Lesson 7: Limits at InfinityLesson 7: Limits at Infinity
Lesson 7: Limits at Infinity
Matthew Leingang
 
1204 ch 12 day 4
1204 ch 12 day 41204 ch 12 day 4
1204 ch 12 day 4
festivalelmo
 
125 5.1
125 5.1125 5.1
125 5.1
Jeneva Clark
 
Lesson 6: Limits Involving Infinity (slides)
Lesson 6: Limits Involving Infinity (slides)Lesson 6: Limits Involving Infinity (slides)
Lesson 6: Limits Involving Infinity (slides)
Matthew Leingang
 
parent functons
parent functonsparent functons
parent functons
Devon Biesterveld
 
Calculus Cheat Sheet All
Calculus Cheat Sheet AllCalculus Cheat Sheet All
Calculus Cheat Sheet All
Moe Han
 
Lesson 4: Calcuating Limits (slides)
Lesson 4: Calcuating Limits (slides)Lesson 4: Calcuating Limits (slides)
Lesson 4: Calcuating Limits (slides)
Matthew Leingang
 
Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)
Matthew Leingang
 
01 Variables And Expressions
01 Variables And Expressions01 Variables And Expressions
01 Variables And Expressions
jsimms
 
Varian, microeconomic analysis, solution book
Varian, microeconomic analysis, solution bookVarian, microeconomic analysis, solution book
Varian, microeconomic analysis, solution book
José Antonio PAYANO YALE
 
Lesson 5: Continuity (slides)
Lesson 5: Continuity (slides)Lesson 5: Continuity (slides)
Lesson 5: Continuity (slides)
Matthew Leingang
 

What's hot (20)

Polynomials
PolynomialsPolynomials
Polynomials
 
Limit - Mohd Noor
Limit - Mohd NoorLimit - Mohd Noor
Limit - Mohd Noor
 
Presentacion calculo jan
Presentacion calculo janPresentacion calculo jan
Presentacion calculo jan
 
Programming exercisesn NUMERICAL ANALYSIS
Programming exercisesn NUMERICAL ANALYSISProgramming exercisesn NUMERICAL ANALYSIS
Programming exercisesn NUMERICAL ANALYSIS
 
Limit of functions
Limit of functionsLimit of functions
Limit of functions
 
Fundamental theorem of algebra
Fundamental theorem of algebraFundamental theorem of algebra
Fundamental theorem of algebra
 
The Definite Integral
The Definite IntegralThe Definite Integral
The Definite Integral
 
Application of derivatives
Application of derivativesApplication of derivatives
Application of derivatives
 
Polynomials
PolynomialsPolynomials
Polynomials
 
Lesson 7: Limits at Infinity
Lesson 7: Limits at InfinityLesson 7: Limits at Infinity
Lesson 7: Limits at Infinity
 
1204 ch 12 day 4
1204 ch 12 day 41204 ch 12 day 4
1204 ch 12 day 4
 
125 5.1
125 5.1125 5.1
125 5.1
 
Lesson 6: Limits Involving Infinity (slides)
Lesson 6: Limits Involving Infinity (slides)Lesson 6: Limits Involving Infinity (slides)
Lesson 6: Limits Involving Infinity (slides)
 
parent functons
parent functonsparent functons
parent functons
 
Calculus Cheat Sheet All
Calculus Cheat Sheet AllCalculus Cheat Sheet All
Calculus Cheat Sheet All
 
Lesson 4: Calcuating Limits (slides)
Lesson 4: Calcuating Limits (slides)Lesson 4: Calcuating Limits (slides)
Lesson 4: Calcuating Limits (slides)
 
Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)
 
01 Variables And Expressions
01 Variables And Expressions01 Variables And Expressions
01 Variables And Expressions
 
Varian, microeconomic analysis, solution book
Varian, microeconomic analysis, solution bookVarian, microeconomic analysis, solution book
Varian, microeconomic analysis, solution book
 
Lesson 5: Continuity (slides)
Lesson 5: Continuity (slides)Lesson 5: Continuity (slides)
Lesson 5: Continuity (slides)
 

More from Tarlan Ahadli

5.2 logistic regression
5.2   logistic regression5.2   logistic regression
5.2 logistic regression
Tarlan Ahadli
 
5.1 logistic regression
5.1   logistic regression5.1   logistic regression
5.1 logistic regression
Tarlan Ahadli
 
3 linear regression deep
3   linear regression deep3   linear regression deep
3 linear regression deep
Tarlan Ahadli
 
2 linear regression intro
2  linear regression intro2  linear regression intro
2 linear regression intro
Tarlan Ahadli
 
1 supervised-unsupervised
1  supervised-unsupervised1  supervised-unsupervised
1 supervised-unsupervised
Tarlan Ahadli
 
Hazardous electromagnetic field
Hazardous electromagnetic fieldHazardous electromagnetic field
Hazardous electromagnetic field
Tarlan Ahadli
 

More from Tarlan Ahadli (6)

5.2 logistic regression
5.2   logistic regression5.2   logistic regression
5.2 logistic regression
 
5.1 logistic regression
5.1   logistic regression5.1   logistic regression
5.1 logistic regression
 
3 linear regression deep
3   linear regression deep3   linear regression deep
3 linear regression deep
 
2 linear regression intro
2  linear regression intro2  linear regression intro
2 linear regression intro
 
1 supervised-unsupervised
1  supervised-unsupervised1  supervised-unsupervised
1 supervised-unsupervised
 
Hazardous electromagnetic field
Hazardous electromagnetic fieldHazardous electromagnetic field
Hazardous electromagnetic field
 

Recently uploaded

Randomised Optimisation Algorithms in DAPHNE
Randomised Optimisation Algorithms in DAPHNERandomised Optimisation Algorithms in DAPHNE
Randomised Optimisation Algorithms in DAPHNE
University of Maribor
 
Sharlene Leurig - Enabling Onsite Water Use with Net Zero Water
Sharlene Leurig - Enabling Onsite Water Use with Net Zero WaterSharlene Leurig - Enabling Onsite Water Use with Net Zero Water
Sharlene Leurig - Enabling Onsite Water Use with Net Zero Water
Texas Alliance of Groundwater Districts
 
Unlocking the mysteries of reproduction: Exploring fecundity and gonadosomati...
Unlocking the mysteries of reproduction: Exploring fecundity and gonadosomati...Unlocking the mysteries of reproduction: Exploring fecundity and gonadosomati...
Unlocking the mysteries of reproduction: Exploring fecundity and gonadosomati...
AbdullaAlAsif1
 
Oedema_types_causes_pathophysiology.pptx
Oedema_types_causes_pathophysiology.pptxOedema_types_causes_pathophysiology.pptx
Oedema_types_causes_pathophysiology.pptx
muralinath2
 
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...
University of Maribor
 
Applied Science: Thermodynamics, Laws & Methodology.pdf
Applied Science: Thermodynamics, Laws & Methodology.pdfApplied Science: Thermodynamics, Laws & Methodology.pdf
Applied Science: Thermodynamics, Laws & Methodology.pdf
University of Hertfordshire
 
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...
Sérgio Sacani
 
Bob Reedy - Nitrate in Texas Groundwater.pdf
Bob Reedy - Nitrate in Texas Groundwater.pdfBob Reedy - Nitrate in Texas Groundwater.pdf
Bob Reedy - Nitrate in Texas Groundwater.pdf
Texas Alliance of Groundwater Districts
 
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...
Travis Hills MN
 
Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdf
Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdfTopic: SICKLE CELL DISEASE IN CHILDREN-3.pdf
Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdf
TinyAnderson
 
The use of Nauplii and metanauplii artemia in aquaculture (brine shrimp).pptx
The use of Nauplii and metanauplii artemia in aquaculture (brine shrimp).pptxThe use of Nauplii and metanauplii artemia in aquaculture (brine shrimp).pptx
The use of Nauplii and metanauplii artemia in aquaculture (brine shrimp).pptx
MAGOTI ERNEST
 
NuGOweek 2024 Ghent programme overview flyer
NuGOweek 2024 Ghent programme overview flyerNuGOweek 2024 Ghent programme overview flyer
NuGOweek 2024 Ghent programme overview flyer
pablovgd
 
aziz sancar nobel prize winner: from mardin to nobel
aziz sancar nobel prize winner: from mardin to nobelaziz sancar nobel prize winner: from mardin to nobel
aziz sancar nobel prize winner: from mardin to nobel
İsa Badur
 
Shallowest Oil Discovery of Turkiye.pptx
Shallowest Oil Discovery of Turkiye.pptxShallowest Oil Discovery of Turkiye.pptx
Shallowest Oil Discovery of Turkiye.pptx
Gokturk Mehmet Dilci
 
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
University of Maribor
 
如何办理(uvic毕业证书)维多利亚大学毕业证本科学位证书原版一模一样
如何办理(uvic毕业证书)维多利亚大学毕业证本科学位证书原版一模一样如何办理(uvic毕业证书)维多利亚大学毕业证本科学位证书原版一模一样
如何办理(uvic毕业证书)维多利亚大学毕业证本科学位证书原版一模一样
yqqaatn0
 
Nucleic Acid-its structural and functional complexity.
Nucleic Acid-its structural and functional complexity.Nucleic Acid-its structural and functional complexity.
Nucleic Acid-its structural and functional complexity.
Nistarini College, Purulia (W.B) India
 
Chapter 12 - climate change and the energy crisis
Chapter 12 - climate change and the energy crisisChapter 12 - climate change and the energy crisis
Chapter 12 - climate change and the energy crisis
tonzsalvador2222
 
The binding of cosmological structures by massless topological defects
The binding of cosmological structures by massless topological defectsThe binding of cosmological structures by massless topological defects
The binding of cosmological structures by massless topological defects
Sérgio Sacani
 
mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốtmô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
HongcNguyn6
 

Recently uploaded (20)

Randomised Optimisation Algorithms in DAPHNE
Randomised Optimisation Algorithms in DAPHNERandomised Optimisation Algorithms in DAPHNE
Randomised Optimisation Algorithms in DAPHNE
 
Sharlene Leurig - Enabling Onsite Water Use with Net Zero Water
Sharlene Leurig - Enabling Onsite Water Use with Net Zero WaterSharlene Leurig - Enabling Onsite Water Use with Net Zero Water
Sharlene Leurig - Enabling Onsite Water Use with Net Zero Water
 
Unlocking the mysteries of reproduction: Exploring fecundity and gonadosomati...
Unlocking the mysteries of reproduction: Exploring fecundity and gonadosomati...Unlocking the mysteries of reproduction: Exploring fecundity and gonadosomati...
Unlocking the mysteries of reproduction: Exploring fecundity and gonadosomati...
 
Oedema_types_causes_pathophysiology.pptx
Oedema_types_causes_pathophysiology.pptxOedema_types_causes_pathophysiology.pptx
Oedema_types_causes_pathophysiology.pptx
 
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...
 
Applied Science: Thermodynamics, Laws & Methodology.pdf
Applied Science: Thermodynamics, Laws & Methodology.pdfApplied Science: Thermodynamics, Laws & Methodology.pdf
Applied Science: Thermodynamics, Laws & Methodology.pdf
 
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...
 
Bob Reedy - Nitrate in Texas Groundwater.pdf
Bob Reedy - Nitrate in Texas Groundwater.pdfBob Reedy - Nitrate in Texas Groundwater.pdf
Bob Reedy - Nitrate in Texas Groundwater.pdf
 
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...
 
Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdf
Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdfTopic: SICKLE CELL DISEASE IN CHILDREN-3.pdf
Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdf
 
The use of Nauplii and metanauplii artemia in aquaculture (brine shrimp).pptx
The use of Nauplii and metanauplii artemia in aquaculture (brine shrimp).pptxThe use of Nauplii and metanauplii artemia in aquaculture (brine shrimp).pptx
The use of Nauplii and metanauplii artemia in aquaculture (brine shrimp).pptx
 
NuGOweek 2024 Ghent programme overview flyer
NuGOweek 2024 Ghent programme overview flyerNuGOweek 2024 Ghent programme overview flyer
NuGOweek 2024 Ghent programme overview flyer
 
aziz sancar nobel prize winner: from mardin to nobel
aziz sancar nobel prize winner: from mardin to nobelaziz sancar nobel prize winner: from mardin to nobel
aziz sancar nobel prize winner: from mardin to nobel
 
Shallowest Oil Discovery of Turkiye.pptx
Shallowest Oil Discovery of Turkiye.pptxShallowest Oil Discovery of Turkiye.pptx
Shallowest Oil Discovery of Turkiye.pptx
 
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...
 
如何办理(uvic毕业证书)维多利亚大学毕业证本科学位证书原版一模一样
如何办理(uvic毕业证书)维多利亚大学毕业证本科学位证书原版一模一样如何办理(uvic毕业证书)维多利亚大学毕业证本科学位证书原版一模一样
如何办理(uvic毕业证书)维多利亚大学毕业证本科学位证书原版一模一样
 
Nucleic Acid-its structural and functional complexity.
Nucleic Acid-its structural and functional complexity.Nucleic Acid-its structural and functional complexity.
Nucleic Acid-its structural and functional complexity.
 
Chapter 12 - climate change and the energy crisis
Chapter 12 - climate change and the energy crisisChapter 12 - climate change and the energy crisis
Chapter 12 - climate change and the energy crisis
 
The binding of cosmological structures by massless topological defects
The binding of cosmological structures by massless topological defectsThe binding of cosmological structures by massless topological defects
The binding of cosmological structures by massless topological defects
 
mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốtmô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
 

4 multivariable linear reg