Transcript Nov 2 - 6: Lecture

CSCI 200 DATA MINING
Introduction to Linear Regression – Predicting
Quality of Wine
Predicting Quality of Wine
• Linear Regression is simple and powerful method
to analyze data and make predictions
• Bordeaux is a region in France popular for
producing wine
• There are differences in price and quality from
year to year that are sometimes very significant
• Bordeaux wines are widely believed to taste
better when they are older.
• There is an incentive to store young wines until
they are mature
Predicting Quality of Wine
• The main issue: it is hard to determine the quality of the
wine when it is so young just by tasting it, since the taste
will change significantly by the time it will be consumed
• Wine testers and experts taste the wine and then predict
which ones will be the best one latest
• Question: can we model this process and make stronger
predictions
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Predicting Quality of Wine
• On March 4, 1990, the New York Times
announced that Princeton Professor of
Economics Orley Ashenfelter can predict the
quality of Bordeaux wine without tasting a single
drop.
• Ashenfelter's predictions have nothing to do with
assessing the aroma of the wine.
• They are the results of a mathematical model.
• Ashenfelter used a method called linear
regression.
Linear Regression
• The methods predicts an outcome variable or
dependent variable.
• It uses a set independent variables.
• Dependent variable: a typical price in 1990-1991
for Bordeaux wine in an auction.
• This approximates quality.
• independent variables: age of the wine-- so the
older wines are more expensive--and weatherrelated information
Linear Regression
• Four independent variables:
• The age of the wine
• The average growing season
temperature
• The harvest rain
• The winter rain
Quality of Wine – Linear Regression
• Professor Ashenfelter believed that his
predictions are more accurate than those of
the world's most influential wine critic,
Robert Parker.
• Robert M. Parker Jr., generally regarded as
the most influential wine critic in America,
calls Professor Ashenfelter's research
''ludicrous and absurd.''
Predicting Quality of Wine - Links
• http://www.wine-
economics.org/workingpapers/AAWE_WP0
4.pdf
• http://www.wine-economics.org/
• http://www.nytimes.com/1990/03/04/us/win
e-equation-puts-some-noses-out-ofjoint.html
One-Variable Linear Regression
• This method uses one independent variable to predict the
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dependent variable
Independent variable: average growing season
temperature (AGST)
The dependent variable, wine price.
The goal of linear regression is to create a predictive line
through the data.
There are many different lines that could be drawn to
predict wine price using average growing season
temperature
Simple Prediction - Average
• The equation for this line:
• y = 7.07
• This linear regression model
would predict 7.07 regardless
of the temperature.
Better Prediction
0.5*Only(AGST)-1.25
• This linear regression model would
predict a higher price when the
temperature is higher.
General Equation
• Y = A*X + B – the model
• X – independent variable (in our case AGST)
• Y- dependent variable (in our case Price)
• Using this equation we will calculate
PREDICTION values
• Model makes Errors
• Y=A*X+B+E
• Error term, E, is also often called a residual.
Y[i]=A*X[i]+B + E[i]
• For each observation, i, we have data for the
dependent variable Yi and data for the
independent variable, Xi.
• Using this equation we make a prediction.
• This prediction is hopefully close to the true
outcome, Yi.
• Since the coefficients have to be the same for all
data points, i, we often make a small error, E[i]
• The best model (choice of A and B) has the
smallest error
SSE – Sum of Squared Errors
•SSE for Average Line
10.15064
•SSE for 0.5*AGST-1.25
6.03251
Better Measures for Regression Quality
• Root Means Squared Error (RMSE):
RMSE = SQRT(SSE/N) (N – is the total number of data points)
• R squared – R2
• R2 compares the best model to a baseline model
• Baseline model – is the model that does not use any
variables - AVERAGE
• The baseline model predicts the average value of the
dependent variable regardless of the value of the
independent variable.
R2
• The sum of squared errors for the baseline model is also
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known as the total sum of squares, commonly referred to
as SST.
In our Example: SST= 10.15
R2 = 1 – SSE/ SST
SSE>=0, SST>=0
SSE<=SST (Y = A*X + B, if A = 0 we get Baseline Model)
Linear regression model will never be worse than the
baseline model.
R2 = 1 – Perfect Predictive Mode
R2 = 0 – No Improvement over the baseline
R2
• R2 is unitless and universally interpretable
between problems.
• However, it can still be hard to compare
between problems.
• Good models for easy problems will have
an R2 close to 1.
• But good models for hard problems can still
have an R2 close to zero.
Regression Model Result
• The line that gives the minimum sum of squared
errors is the line that regression model will find.
• Formula for the Linear Regression Model:
• Y = 0.63509*AGST-3.4178
• R2 = 0.43502
• SSE = 5.73488