COMPSCI C8 Lecture Notes - Lecture 37: Simple Linear Regression, Multicollinearity

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Regression methods: simple linear regression, predict using only one quantitative attribute, find a slope and intercept to minimize squared error, multiple (linear) regression, predict using multiple quantitative attributes, find many slopes to minimize squared error. To predict a house price from its size (x1) and age (x2) A multiple (linear) regression prediction has this form: (a1 $/sqft) * (x1 sqft of space) + (a2 $/yr) * (x2 yrs old) + b. A1 and a2 are both slopes of a line in 3d. Each slope describes how much the mean house price increases/decreases for each increase of 1 in an attribute. The slopes (and intercept) can be chosen together to minimize squared error on training examples. Slopes are hard to interpret because of multicollinearity. Very different slopes can give nearly the same error. For estimates to be reliable across the range of possible inputs, we require a linear association in the population.

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