12.1 - 12.3 Predicting the Outcome of a Variable

Question 1

Define the (least squares) regression line. What is the equation?

Answer 1

requires that the sum of the squares of the vertical distances from the data points (x, y) to the line is as small as possible
only for linear associations
y = mx+b
-y = responding variable
-x = explanatory variable
-m = slope = the amount that ŷ changes when x increases by 1 unit
-b = y-intercept = the prediced value of ŷ when x=0
NOT resistant to outliers

Question 2

Define interpolating. Define exterpolating.

Answer 2

*interpolating - predicting ŷ for x-values that are BETWEEN observed x-values; can produce unrealistic forecasts
*exterpolating - predicting ŷ for x-values that are BEYOND observed x-values

Question 3

What is r^2?

Answer 3

the strength of the correlation squared; NOT resistant to outliers
“48% of the variation in [the response variable, y] can be explained by the variation in [the explanatory variable, x]”

Question 4

Define slope of the regression line.

Answer 4

the amount that ŷ changes when x increases by 1 unit

Question 5

Define y-int of the regression line.

Answer 5

the predicted value of ŷ when x=0

Question 6

Define residual.

Answer 6

the difference between the actual value and the predicted value (y - ŷ)