Linear Regression Model Overview
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Questions and Answers

What type of function is the example quadratic function?

  • Exponential function
  • Logarithmic function
  • Multivariate function
  • Univariate function (correct)
  • What is the formula for the gradient function of the given quadratic function?

  • $5x - 3$
  • $2x$ (correct)
  • $x + 1$
  • $x^2$
  • How does the step size (learning rate) affect the convergence of the gradient descent algorithm for the quadratic function?

  • Larger learning rate leads to larger steps and slower convergence
  • Smaller learning rate leads to smaller steps and slower convergence (correct)
  • Smaller learning rate leads to larger steps and faster convergence
  • Larger learning rate leads to smaller steps and faster convergence
  • Which of the following is not a way to evaluate a machine learning model's performance?

    <p>Coefficient of Determination (R-squared)</p> Signup and view all the answers

    What is the definition of bias in the context of machine learning models?

    <p>The error or difference between the model's predictions and the actual values</p> Signup and view all the answers

    What is the primary cause of bias in a machine learning model?

    <p>Wrong assumptions in the machine learning process</p> Signup and view all the answers

    What do the βj's represent in the linear regression model?

    <p>Unknown parameters or coefficients</p> Signup and view all the answers

    Which of the following is an example of a polynomial representation in the linear regression model?

    <p>X3 = X1^2</p> Signup and view all the answers

    What do interaction terms like X3 = X1 * X2 represent in the linear regression model?

    <p>Interactions between variables</p> Signup and view all the answers

    Which of the following is an example of a transformation of a quantitative input in the linear regression model?

    <p>X3 = log(X1)</p> Signup and view all the answers

    What is the purpose of dummy coding for qualitative inputs in the linear regression model?

    <p>To represent the effect of a qualitative input by a set of level-dependent constants</p> Signup and view all the answers

    In the simple linear regression model, what is assumed about the relationship between the predictor variable X and the response variable Y?

    <p>There is approximately a linear relationship between X and Y</p> Signup and view all the answers

    What do the symbols β0 and β1 represent in the linear model sales ≈ β0 + β1 × TV?

    <p>β0 represents the intercept and β1 represents the slope</p> Signup and view all the answers

    What does the hat symbol (^) denote in the expression $\hat{\beta}_0$ and $\hat{\beta}_1$?

    <p>It denotes the estimated value for the unknown parameters</p> Signup and view all the answers

    What is the goal when estimating the coefficients β0 and β1 using the data (x1, y1), (x2, y2), ..., (xn, yn)?

    <p>To find values of β0 and β1 that minimize the sum of squared residuals</p> Signup and view all the answers

    If the linear model is extended to include a quadratic term for TV, what would the model equation look like?

    <p>sales ≈ β0 + β1 × TV + β2 × TV^2</p> Signup and view all the answers

    Suppose the model includes an interaction term between TV and another variable, say Radio. How would the model equation look?

    <p>sales ≈ β0 + β1 × TV + β2 × Radio + β3 × TV × Radio</p> Signup and view all the answers

    If the input variable TV is transformed using a logarithmic function, how would the model equation change?

    <p>sales ≈ β0 + β1 × log(TV)</p> Signup and view all the answers

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