Regression (Exam 1)

Question 1

regression line

Answer 1

• a straight line that describes how a response variable y changes as an explanatory variable x changes in a linear relationship
• interprets (can describe how y varies with x)
• predicts (can predict the value of y for a given value of x) the future
• equation: ŷ = b0 + b1x

Question 2

prediction error (“residual”)

Answer 2

• how far away the predicted response is from the observed (actual) response
• error = observed – predicted = y – ŷ
• vertical distance between the points and the regression line

Question 3

least squares regression line

Answer 3

• want to choose the line that makes the errors (vertical distances) as small as possible
• the line that minimizes the sum of the squared errors
• focus on the magnitude of the error

Question 4

what are some cautions regarding regression?

Answer 4

• only for linear relationships
• association ≠ causation
• lurking variables
• influential points/outliers
• extrapolation

Question 5

influential

Answer 5

• if removing it from the analysis would significantly change the result of a statistical calculation
• outliers in the x-direction, y-direction, or relationship are often influential for the regression equation

Question 6

extrapolation

Answer 6

• a prediction for an x that is far away from the x’s in the dataset
• can be dangerous, because they assume the same linear relationship holds for values far outside of the range of data set used to build the model