Lecture 8 Flashcards
What is the equation for the correlation coefficient?
r = 1/n En i=1 (x_i - xbar / σ_x) * (y_i - ybar / σ_y)
What is R_sq(w_0, w_1)?
σ_y^2(1 - r^2)
What do we often use to compare the performances of different models in machine learning?
the mean squared error and r^2
What is the equivalent of finding models that minimize the mean squared error?
finding models that maximize r^2
What is the simple linear regression model similar to?
the constant model except it is more flexible
What will help us to use linear regression but with multiple features and nonlinearity?
matrices and vectors
If two matrices A and B, what is not true?
AB ≠ BA
What is a vector in R^n?
an ordered collection of n numbers
How do we usually write vectors?
as columns
How do we usually write vectors?
lower-case letters with an arrow on top
What is another way of writing a vector?
[1, 2, 3 , 4]^T
If a vector v has four components, how do we write that?
varrow E R^4
What is another way to say the length of a vector?
the L_2 norm
What is the L_2 norm of a vector v?
||v|| = sqrt(v_1^2 + v_2^2 + … + v_n^2)
What is a vector sometimes described as?
an object with a magnitude/length and direction
