Introduction to Linear Regression

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What is the significance of the hat symbol (ˆ) in the equation yˆi = f(xˆi) = ŵxi + b̂?

It indicates the estimated values of the model parameters (correct)

It indicates the error between the predicted and actual values

It indicates the predicted values of x and y

It indicates the true values of x and y

What is the primary goal when using linear regression?

To visualize the data in a higher-dimensional space

To reduce the dimensionality of the input data

To find the most accurate values for ŵ and b̂ (correct)

To determine the relationship between multiple input variables

What is the relationship between x and y in linear regression?

y is a non-linear function of x

y is a linear function of x (correct)

y is inversely proportional to x

y is proportional to the square of x

What is the purpose of step 2 in the linear regression algorithm?

To calculate the error from the current line Signup and view all the answers

What is the purpose of starting with a random line in step 1 of the linear regression algorithm?

To provide an initial estimate of the model parameters Signup and view all the answers

What is the role of the variables w and b in the linear regression equation?

They are the model parameters, where w is the slope and b is the intercept Signup and view all the answers

What is the primary goal of regression in machine learning?

To estimate a relationship between dependent and independent variables Signup and view all the answers

In the context of regression, what do the x's represent?

The input values of the independent variables Signup and view all the answers

What is the notation used to represent a single data point in a regression dataset?

(x, y)(i) Signup and view all the answers

What is an example of an independent variable in the context of house prices?

The square footage of the house Signup and view all the answers

What is the term for the number of data points in a regression dataset?

n Signup and view all the answers

What is the primary assumption of regression?

The relationship between the variables is linear Signup and view all the answers

What is the assumption made about the relationship between y and x in linear regression?

y is approximately equal to f(x) Signup and view all the answers

What is the true function f in linear regression?

A function that exists in the real world that maps input to output Signup and view all the answers

What is the purpose of defining a model fˆ in linear regression?

To be as close as possible to the true function f Signup and view all the answers

What is the relationship between x and y in the equation y ≈ f(x)?

y is dependent on x Signup and view all the answers

What is the notation R used for in the context of linear regression?

The set of all real numbers Signup and view all the answers

What is the implication of the assumption that y ≈ f(x)?

There is a deterministic relationship between x and y Signup and view all the answers

Introduction to Linear Regression

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