STSCI 3740 Lecture 4

What is the main purpose of linear regression in supervised learning?

• To classify data into different categories.

• To predict a quantitative response.

• To find the median value of a dataset.

• To reduce the dimensions of the data.

What is the general form of a simple linear regression model?

• Y=β0​+ϵ

• Y=β0​+β1​X+ϵ

• Y=β1​X+ϵ

• Y=ϵ+β0​

In the linear regression model Y=β0+β1X+ϵ, what do β0 and β1 represent?

• The variance and standard deviation of the error term.

• The mean and median of the predicted variable.

• The intercept and slope of the regression line, respectively.

• • The coefficients of the independent variables.

What is the least squares approach in linear regression?

• Maximizing the sum of the residuals.

• Dividing the residual sum by the number of observations.

• Minimizing the residual sum of squares (RSS).

• Finding the median of the residuals.

Which of the following is the correct expression for the residual sum of squares (RSS) in linear regression?

• RSS=∑​(Xi​−Yi​)2

• RSS=∑ (Yi​−^Yi​)2

• RSS=∑ ​(Yi​−β0​)2

• RSS=∑​(Yi​−β1​)2

How would you interpret a slope β1​ in a simple linear regression?

• It represents the value of the dependent variable when X=0

• It represents the total number of observations in the dataset.

• It represents the change in the dependent variable Y for a one-unit increase in the independent variable X.

• It represents the intercept of the regression line.