regression - university of washington€¦ · 3/27/18 5 9 ©2018 emily fox stat/cse 416: intro to...
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3/27/18
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STAT/CSE 416: Intro to Machine Learning
Regression:Predicting House PricesEmily FoxUniversity of WashingtonMarch 27, 2018
1 ©2018 Emily Fox
STAT/CSE 416: Intro to Machine Learning
Predicting house prices
©2018 Emily Fox2
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How much is my house worth?
©2018 Emily Fox
I want to listmy house
for sale
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How much is my house worth?
©2018 Emily Fox
$$ ????
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STAT/CSE 416: Intro to Machine Learning
Data
©2018 Emily Fox
(x1 = sq.ft., y1 = $)
(x2 = sq.ft., y2 = $)
(x3 = sq.ft., y3 = $)
(x4 = sq.ft., y4 = $) Input vs. Output:• y is the quantity of interest
• assume y can be predicted from x
input output
…
(x5 = sq.ft., y5 = $)
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Look at recent sales in my neighborhood
How much did they sell for?
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Plot recent house sales (Past 2 years)
©2018 Emily Fox
square feet (sq.ft.)
pri
ce ($
)
x
y
Terminology:x – feature,
covariate, or predictor
y – observation or response
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Predict your house by similar houses
©2018 Emily Fox
square feet (sq.ft.)
pri
ce ($
)
x
y
No house sold recently had exactlythe same sq.ft.
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STAT/CSE 416: Intro to Machine Learning9 ©2018 Emily Fox
square feet (sq.ft.)
pri
ce ($
)
x
y
• Look at average price in range
• Still only 2 houses!• Throwing out info
from all other sales
Predict your house by similar houses
STAT/CSE 416: Intro to Machine Learning10 ©2018 Emily Fox
square feet (sq.ft.)
pri
ce ($
)
x
y
Model – How we assume the world works
Regression model:
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STAT/CSE 416: Intro to Machine Learning11 ©2018 Emily Fox
square feet (sq.ft.)
pri
ce ($
)
x
y
“Essentially, all models are wrong, but some are useful.”
George Box, 1987.
Model – How we assume the world works
STAT/CSE 416: Intro to Machine Learning12 ©2018 Emily Fox
TrainingData
Featureextraction
ML model
Qualitymetric
ML algorithm
y
x ŷ
⌃f
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STAT/CSE 416: Intro to Machine Learning
Linear regression
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STAT/CSE 416: Intro to Machine Learning14 ©2018 Emily Fox
TrainingData
Featureextraction
ML model
Qualitymetric
ML algorithm
y
x ŷ
f⌃
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STAT/CSE 416: Intro to Machine Learning15 ©2018 Emily Fox
square feet (sq.ft.)
pri
ce ($
)
x
yFit a line through the data
f(x) = w0+w1 x
parameters of model
Use a simple linear regression model
yi = w0+w1 xi + εi
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Which line?
©2018 Emily Fox
square feet (sq.ft.)
pri
ce ($
)
x
y
different parameters w0,w1
f(x) = w0+w1 x
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STAT/CSE 416: Intro to Machine Learning17 ©2018 Emily Fox
TrainingData
Featureextraction
ML model
Qualitymetric
ML algorithm
ŵy
x ŷ
f⌃
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“Cost” of using a given line
©2018 Emily Fox
square feet (sq.ft.)
pri
ce ($
)
x
y Residual sum of squares (RSS)
RSS(w0,w1) = ($house 1-[w0+w1sq.ft.house 1])2
+ ($house 2-[w0+w1sq.ft.house 2])2
+ ($house 3-[w0+w1sq.ft.house 3])2
+ … [include all houses]