Method of Least Squares

STAT 20: Introduction to Probability and Statistics

Linear Models Review

Go to pollev.com and get ready for a kahoot-style quiz!

Concept Questions

Concept Question 1

An engineer working for Waymo self-driving cars is working to solve a problem. When it rains, reflections of other cars in puddles can disorient the self-driving car. Their team is working on a model to determine when the self-driving car is seeing a reflection of a car vs a real car.

Think of a potential response and predictor, and about whether this is a regression or classification problem.

01:00

This is a serious challenge encountered by self-driving cars at the moment. This is probably best thought of as a classification problem, with the response being either reflection / not or puddle / not. The predictors could be sensor input (cameras, lidar) as well as weather info (to know if it’s been raining).

Concept Question 2

An analyst working for the UC Berkeley Admissions Office is working to help the university decide how many students to send offer letters to. They have a target class size (that fits within the budget and residence halls), but they’re not sure how many students will accept the offer. How many should they admit?

Think of a potential response and predictor, and about whether this is a regression or classification problem.

01:00

This is another very real task. Universities use what’s called a “yield model” to predict whether or not a student will accept the offer. That’s a classification method. Those classifiers aggregated up across all offers lead to a numerical prediction for the total yield, which looks more like a regression problem, so either answer could work. It could also be a direct regression model where they use aggregate stats of the class to predict the total yield.

Response is either the decision of a single student or the total number of students that accept. Predictors could be either student level covariates (for classification) or class-level averages (for regression). Those might also include broader economic indicators like unemployment rate.

Concept Question 3

• Here is a function f.

f <- function(x, y) {
  y*(x + 3) 
}

What will the following line of code return?

f(3,5)

This question reminds students that if function arguments are unnamed, they are assumed to have been input in the order they were originally specified as in the function definition. x will be assigned 3, and y will be assigned 5, so the correct answer is 30.