Week 9 Linear Regression Flashcards
Name the 2 types of relationships in linear regression
- Deterministic (or functional) relationship
- Statistical relationship
The relationship between Celsius and Fahrenheit would be described as a ___________ relationship
Deterministic (or functional)
The relationship between Celsius and Fahrenheit would be described as a ___________ relationship
Deterministic (or functional)
If you graph a deterministic relationship, where will the relationships line fall?
Directly on the data points
The relationship between height and weight would be described as a _________ relationship
Statistical
Name this relationship: Alcohol consumed and blood alcohol content
Statistical
Name this relationship: Speed and gas mileage
Statistical (As speed increases you would expect gas mileage to decrease)
Name this relationship: Speed and gas mileage
Statistical (As speed increases you would expect gas mileage to decrease)
In this relationship, the equation exactly describes the relationship between the two variables
Deterministic
When do you use Regression?
When you have a series of continuous data that follows some sort of pattern
Regression determines the _______ of the ____________ between the dependent variable and a series of other variables (known as ___________ variables)
strength of the relationship, independent
Name this type of regression: ALlows us to summarize and study relationships between two continuous variables
Simple linear
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
independent, dependent
This variable is known as the predictor
independent variable
This variable is known as the response
dependent variable
For a single line, Linear regression uses these parameters
h(x) = Θ0 + Θ1 x
What is this the equivalent of?
y = mx + b
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
Linear regression with one variable
What else is linear regression with one variable called?
Univariate linear regression
How are the best Θ0 and Θ1 values chosen for linear regression?
They chosen using a cost function
How does a cost function work?
The total error is calculated between the predicted values and actual values.
We continue to change the values until we find the minimum error.
A line that fits the data “best” will be the one with the
minimum amount of prediction errors
What we use to find the overall prediction error?
the least squares criterion
To measure accuracy we can calculate the “Coefficient of determination”, which is also called the residual or r^2
What does r represent?
The correlation coefficient
What is the range of r^2?
It’s a number between 0 and 1
What does it mean if r^2 is higher? What does it mean if it’s lower?
The closer to 1, the closer the data is to the line. The closer to 0, the further the data is from the line
In a multiple regression model, what does each number mean next to the variable?
The strength/type of relationships each variable has with the class variable.
Type = whether it’s positive or negative
Is multivariate regression the same as multiple regression? How?
No.
Multivariate = multiple dependent variables, possible multiple independent variables
Multiple regression = single dependent variable, multiple independent variables
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
Logistic regression
