18 Questions
What type of function is the example quadratic function?
Univariate function
What is the formula for the gradient function of the given quadratic function?
$2x$
How does the step size (learning rate) affect the convergence of the gradient descent algorithm for the quadratic function?
Smaller learning rate leads to smaller steps and slower convergence
Which of the following is not a way to evaluate a machine learning model's performance?
Coefficient of Determination (R-squared)
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
What is the primary cause of bias in a machine learning model?
Wrong assumptions in the machine learning process
What do the βj's represent in the linear regression model?
Unknown parameters or coefficients
Which of the following is an example of a polynomial representation in the linear regression model?
X3 = X1^2
What do interaction terms like X3 = X1 * X2 represent in the linear regression model?
Interactions between variables
Which of the following is an example of a transformation of a quantitative input in the linear regression model?
X3 = log(X1)
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
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
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
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
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
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
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
If the input variable TV is transformed using a logarithmic function, how would the model equation change?
sales ≈ β0 + β1 × log(TV)
This quiz provides an overview of the linear regression model and its application in predicting real-valued outputs based on input features. It explores the concept of unknown parameters, coefficients, and the linearity assumption in the regression function.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
