7.4 Confidence Intervals for Variance and Standard Deviation
Lecture 19 · 2020. 8. 24. · Residual Variance The mean of residuals is always 0, regardless of...
Transcript of Lecture 19 · 2020. 8. 24. · Residual Variance The mean of residuals is always 0, regardless of...
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190F Spring 2020
Foundations of Data Science
Lecture 19 Residuals
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Announcements
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Residuals
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Residuals ● Error in regression estimate
● One residual corresponding to each point (x, y)
● residual = observed y - regression estimate of y = observed y - height of regression
line at x = vertical difference between point
and line (Demo)
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Residual Plot A scatter diagram of residuals
● Should look like an unassociated blob for linear relations
● But still contains patterns for non-linear relations
● Used to check whether linear regression is appropriate
(Demo)
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Regression Diagnostics
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Dugong
(Demo)
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Properties of Residuals
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Residual Variance The mean of residuals is always 0, regardless of the original data
Variance is standard deviation squared: mean squared deviation
(Variance of residuals) / (Variance of y) = 1 - r2
(Variance of fitted values) / (Variance of y) = r2
Variance of y = (Variance of fitted values) + (Variance of residuals)
(Demo)
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Discussion Question How does the SD of the fitted values relate to r?
A. (SD of fitted) / (SD of y) = r
B. (SD of fitted) / (SD of y) = |r|
C. (SD of fitted) / (SD of residuals) = r
D. (SD of fitted) / (SD of residuals) = |r|
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Regression Model
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A “Model”: Signal + Noise
Distance drawn at random from normal distribution with mean 0
Another distance drawn independently from the same normal distribution
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What We Get to See
(Demo)