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AP Statistics Section 3.2 A Regression Lines.

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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.

regression line

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 __________.

slope

y-intercept

Once you have computed b, you can then find the value of a using this equation.

Interpreting b: The slope b is the predicted _____________ in the response variable y as the explanatory variable x changes.

rate of change

The slope b = -.0034 tells

us that fat gain goes down by .0034 kg for each additional calorie of NEA.

You cannot say how important a relationship is by looking at how big the regression slope is.

Interpreting a:The y-intercept a= 3.505 kg is the fat gain estimated by the model if

NEA does not change when a person overeats.

Prediction: Predict the fat gain for an individual whose NEA increases by 400 cal by:(a) using the graph ___________(b) using the equation _________

Prediction: Predict the fat gain for an individual whose NEA increases by 400 cal by:(a) using the graph ___________(b) using the equation _________

Prediction: Predict the fat gain for an individual whose NEA increases by 400 cal by:(a) using the graph ___________(b) using the equation _________

So we are predicting that this individual loses fat when he/she overeats. What went wrong?

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.

b

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