Linear Regression Model Overview

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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?

Coefficient of Determination (R-squared) (C) Signup and view all the answers

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

The error or difference between the model's predictions and the actual values (B) Signup and view all the answers

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

Wrong assumptions in the machine learning process (D) Signup and view all the answers

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

Unknown parameters or coefficients (C) Signup and view all the answers

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

X3 = X1^2 (A) Signup and view all the answers

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

Interactions between variables (C) 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?

X3 = log(X1) (B) Signup and view all the answers

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

To represent the effect of a qualitative input by a set of level-dependent constants (A) 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?

There is approximately a linear relationship between X and Y (B) Signup and view all the answers

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

β0 represents the intercept and β1 represents the slope (B) Signup and view all the answers

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

It denotes the estimated value for the unknown parameters (D) 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)?

To find values of β0 and β1 that minimize the sum of squared residuals (D) 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?

sales ≈ β0 + β1 × TV + β2 × TV^2 (A) 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?

sales ≈ β0 + β1 × TV + β2 × Radio + β3 × TV × Radio (C) Signup and view all the answers

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

sales ≈ β0 + β1 × log(TV) (D) Signup and view all the answers