Lecture 12 Flashcards
What is linear regression with multiple features called?
multiple linear regression
How many dimensions do we need to graph a multiple linear regression model?
3 because we need a plane
How would we find the prediction plane for multiple linear regression?
the plane of best fit that pierces through the cloud points
What are training examples?
n individuals
How do we distinguish between features?
with the use of superscripts where we have d features
What is the augmented feature vector Aug(x)?
the vector obtained by a adding a 1 to the front of feature vector x
What is the equivalent of w * Aug(x)?
w_0 + w_1x^(1) + w_2x^(2) + … + w_dx^(d)
What happens when w has d features?
it has d + 1 entries
What do w_1, w_2, …, w_d each give?
weight/coefficient/slope/feature
If we are trying to predict sales for stores, what will the signs of w1* and w2* be?
w1* (square feet) will be + and w2* (competitors) will be -
What do we have to do if we care about interpretability of resulting weights?
standardize each feature before performing regression
How do we convert features to standard units?
x_i - mean / std of x
How do we calculate standard deviation?
sqrt(1/n (x_i - mean)^2)
What can we not standardize?
the column of all 1s
What can we directly compare to one another?
standardized regression coefficients
