Introduction to Linear Regression
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Questions and Answers

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?

    <p>To calculate the error from the current line</p> Signup and view all the answers

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

    <p>To provide an initial estimate of the model parameters</p> Signup and view all the answers

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

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

    What is the primary goal of regression in machine learning?

    <p>To estimate a relationship between dependent and independent variables</p> Signup and view all the answers

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

    <p>The input values of the independent variables</p> Signup and view all the answers

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

    <p>(x, y)(i)</p> Signup and view all the answers

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

    <p>The square footage of the house</p> Signup and view all the answers

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

    <p>n</p> Signup and view all the answers

    What is the primary assumption of regression?

    <p>The relationship between the variables is linear</p> Signup and view all the answers

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

    <p>y is approximately equal to f(x)</p> Signup and view all the answers

    What is the true function f in linear regression?

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

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

    <p>To be as close as possible to the true function f</p> Signup and view all the answers

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

    <p>y is dependent on x</p> Signup and view all the answers

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

    <p>The set of all real numbers</p> Signup and view all the answers

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

    <p>There is a deterministic relationship between x and y</p> Signup and view all the answers

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