AP Statistics Section 3.2 A Regression Lines.
Linear relationships between two quantitative variables are quite common. Correlation measures the direction and strength of these relationships. Just as we drew a density curve to model the data in a histogram, we can summarize the overall pattern in a linear relationship by drawing a _______________ on the scatterplot.
Note that regression requires that we have an explanatory variable and a response variable. A regression line is often used to predict the value of y for a given value of x.
Who:______________________________What:______________________________ ______________________________Why:_______________________________When, where, how and by whom? The data come from a controlled experiment in which subjects were forced to overeat for an 8-week period. Results of the study were published in Science magazine in 1999.
16 healthy young adults
Exp.-change in NEA (cal)
Resp.-fat gain (kg)
Do changes in NEA explain weight gain
Numerical summary: The correlation between NEA change and fat gain is r = _______
A least-squares regression line relating y to x has an equation of the form ___________In this equation, b is the _____, and a is the __________.
rate of change
us that fat gain goes down by .0034 kg for each additional calorie of NEA.
NEA does not change when a person overeats.
1500 is way outside the range of NEA values in our data
Extrapolation is the use of a regression line for prediction outside the range of values of the explanatory variable x used to obtain the line. Such predictions are often not accurate.