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# Introduction to Linear Regression

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@PremierJacksonville

### 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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