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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.

regression line


Ap statistics section 3 2 a regression lines

Note that regression 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 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.


Ap statistics section 3 2 a regression lines

Who:______________________________ 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 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


Ap statistics section 3 2 a regression lines

8 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

6

4

2

0

F

a

t

G

a

i

n

(kg)

-100 0 100 200 300 400 500 600 700

NEA (calories)


Ap statistics section 3 2 a regression lines

8 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

6

4

2

0

F

a

t

G

a

i

n

(kg)

-100 0 100 200 300 400 500 600 700

NEA (calories)


Ap statistics section 3 2 a regression lines

Numerical summary: 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 The correlation between NEA change and fat gain is r = _______


Ap statistics section 3 2 a regression lines

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




Ap statistics section 3 2 a regression lines
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
The slope b = -.0034 tells

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



Interpreting a the y intercept a 3 505 kg is the fat gain estimated by the model if
Interpreting how big the regression slope is.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.


Model using the equation above draw the lsl on your scatterplot
Model: how big the regression slope is. Using the equation above, draw the LSL on your scatterplot.


Ap statistics section 3 2 a regression lines

8 how big the regression slope is.

6

4

2

0

F

a

t

G

a

i

n

(kg)

-100 0 100 200 300 400 500 600 700

NEA (calories)


Ti 83 84 8 linreg a bx graph
TI 83/84 how big the regression slope is. 8:LinReg(a+bx) GRAPH


Ap statistics section 3 2 a regression lines

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


Ap statistics section 3 2 a regression lines

8 how big the regression slope is.

6

4

2

0

F

a

t

G

a

i

n

(kg)

-100 0 100 200 300 400 500 600 700

NEA (calories)


Ap statistics section 3 2 a regression lines

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


Ap statistics section 3 2 a regression lines

Prediction: how big the regression slope is. 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
So we are predicting that this individual by 1500 calloses fat when he/she overeats. What went wrong?

1500 is way outside the range of NEA values in our data


Ap statistics section 3 2 a regression lines

Extrapolation by 1500 cal 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.


Ap statistics section 3 2 a regression lines

a by 1500 cal

b