modeling, SLR

Question 1

regression line formula

Answer 1

y hat = a hat + b hat * x

Question 2

What is MSE and how is it used?

Answer 2

MSE = mean squared
MSE(a, b) = 1/n E(sub i)(yi - yi hat(a, b))^2

Question 3

slope and intercept formula from data 8?

Answer 3

slope = r * (SD of y/ SD of x)
intercept = avg of y - avg of x * slope

Question 4

SLR Model

Answer 4

y hat = a + bx

Question 5

What is a loss function?

Answer 5

A loss function characterizes the cost, error, or fit
resulting from a particular choice of model or model parameters

Question 6

Squared Loss (L2)

Answer 6

L(y, yhat) = (y-yhat)^2

Question 7

Absolute Loss(L1)

Answer 7

L(y, yhat) = | y - yhat |

Question 8

What is empirical risk / average loss?

Answer 8

We care about how bad our model’s predictions are for our entire data set, not just for one point. A natural measure, then, is of the average loss (aka empirical risk) across all points.

Question 9

How do we minimize the MSE?

Answer 9

MSE(a, b) = 1/nE(sub i)(yi - a - bxi)2

**To find the best values, we take derivatives with respect to the choice variables (a, b)