Week 9 Linear Regression

Question 1

Name the 2 types of relationships in linear regression

Answer 1

1. Deterministic (or functional) relationship
2. Statistical relationship

Question 2

The relationship between Celsius and Fahrenheit would be described as a ___________ relationship

Answer 2

Deterministic (or functional)

Question 3

The relationship between Celsius and Fahrenheit would be described as a ___________ relationship

Answer 3

Deterministic (or functional)

Question 4

If you graph a deterministic relationship, where will the relationships line fall?

Answer 4

Directly on the data points

Question 5

The relationship between height and weight would be described as a _________ relationship

Answer 5

Statistical

Question 6

Name this relationship: Alcohol consumed and blood alcohol content

Answer 6

Statistical

Question 7

Name this relationship: Speed and gas mileage

Answer 7

Statistical (As speed increases you would expect gas mileage to decrease)

Question 8

Name this relationship: Speed and gas mileage

Answer 8

Statistical (As speed increases you would expect gas mileage to decrease)

Question 8

In this relationship, the equation exactly describes the relationship between the two variables

Answer 8

Deterministic

Question 9

When do you use Regression?

Answer 9

When you have a series of continuous data that follows some sort of pattern

Question 10

Regression determines the _______ of the ____________ between the dependent variable and a series of other variables (known as ___________ variables)

Answer 10

strength of the relationship, independent

Question 11

Name this type of regression: ALlows us to summarize and study relationships between two continuous variables

Answer 11

Simple linear

Question 12

In simple linear regression we have one variable denoted as x, which is the ________ variable, and a variable denoted as y, which is the ________ variable

Answer 12

independent, dependent

Question 13

This variable is known as the predictor

Answer 13

independent variable

Question 14

This variable is known as the response

Answer 14

dependent variable

Question 15

For a single line, Linear regression uses these parameters

h(x) = Θ0 + Θ1 x

What is this the equivalent of?

Answer 15

y = mx + b

Question 16

Name this: A single line that is the best-fit line to a data set. The line is then used to predict real values for continuous output

Answer 16

Linear regression with one variable

Question 17

What else is linear regression with one variable called?

Answer 17

Univariate linear regression

Question 18

How are the best Θ0 and Θ1 values chosen for linear regression?

Answer 18

They chosen using a cost function

Question 19

How does a cost function work?

Answer 19

The total error is calculated between the predicted values and actual values.

We continue to change the values until we find the minimum error.

Question 20

A line that fits the data “best” will be the one with the

Answer 20

minimum amount of prediction errors

Question 21

What we use to find the overall prediction error?

Answer 21

the least squares criterion

Question 22

To measure accuracy we can calculate the “Coefficient of determination”, which is also called the residual or r^2

What does r represent?

Answer 22

The correlation coefficient

Question 23

What is the range of r^2?

Answer 23

It’s a number between 0 and 1

Question 24

What does it mean if r^2 is higher? What does it mean if it’s lower?

Answer 24

The closer to 1, the closer the data is to the line. The closer to 0, the further the data is from the line

Question 25

In a multiple regression model, what does each number mean next to the variable?

Answer 25

The strength/type of relationships each variable has with the class variable.

Type = whether it’s positive or negative

Question 26

Is multivariate regression the same as multiple regression? How?

Answer 26

No.

Multivariate = multiple dependent variables, possible multiple independent variables

Multiple regression = single dependent variable, multiple independent variables

Question 27

Name this: Models a relationship between independent (predictor) variables and a categorical response variable

Through this we can estimate the probability of falling into a certain level of the categorical response, given a set of predictors

Answer 27

Logistic regression