CORRELATION AND REGRESSION DR. GHADA ABO-ZAID Correlation and regression.
AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative...
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Transcript of AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative...
![Page 1: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/1.jpg)
AP Statistics Section 3.2 ARegression Lines
![Page 2: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/2.jpg)
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
![Page 3: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/3.jpg)
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.
![Page 4: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/4.jpg)
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 adultsExp.-change in NEA (cal)Resp.-fat gain (kg)
Do changes in NEA explain weight gain
![Page 5: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/5.jpg)
NEA (calories)
Fat
Gain
(kg)
-100 0 100 200 300 400 500 600 700
8
6
4
2
0
![Page 6: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/6.jpg)
NEA (calories)
Fat
Gain
(kg)
-100 0 100 200 300 400 500 600 700
8
6
4
2
0
![Page 7: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/7.jpg)
Numerical summary: The correlation between NEA
change and fat gain is r = _______
7786.
![Page 8: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/8.jpg)
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 __________.
bxay ˆ
slopey-intercept
![Page 9: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/9.jpg)
The formula at the right will allow you to find the value of b:
x
y
SS
rb
![Page 10: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/10.jpg)
Once you have computed b, you can then find the value of a using
this equation.
)(xbya
![Page 11: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/11.jpg)
We can also find these values on our TI-83/84.
earlierr found way wesame
![Page 12: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/12.jpg)
For this example, the LSL is
or
xy 0034.505.3ˆ
.))((0034.505.3)( calNEAchangekgFatGain
![Page 13: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/13.jpg)
Interpreting b: The slope b is the predicted _____________ in the
response variable y as the explanatory variable x changes.
rate of change
![Page 14: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/14.jpg)
The slope b = -.0034 tells
us that fat gain goes down by .0034 kg for each additional
calorie of NEA.
![Page 15: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/15.jpg)
You cannot say how important a relationship is by looking at how
big the regression slope is.
![Page 16: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/16.jpg)
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.
![Page 17: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/17.jpg)
Model: Using the equation above, draw the LSL on your scatterplot.
![Page 18: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/18.jpg)
NEA (calories)
Fat
Gain
(kg)
-100 0 100 200 300 400 500 600 700
8
6
4
2
0
5007.1
10034.
10000340034.
![Page 19: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/19.jpg)
TI 83/84 8:LinReg(a+bx)
GRAPH
121 ,, YLL
ENTERYFunctionVARSY
VARS
1:1:1
![Page 20: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/20.jpg)
Prediction: Predict the fat gain for an individual whose NEA increases
by 400 cal by:
(a) using the graph ___________
(b) using the equation _________
![Page 21: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/21.jpg)
NEA (calories)
Fat
Gain
(kg)
-100 0 100 200 300 400 500 600 700
8
6
4
2
0
![Page 22: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/22.jpg)
Prediction: Predict the fat gain for an individual whose NEA increases
by 400 cal by:
(a) using the graph ___________
(b) using the equation _________
2.2
![Page 23: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/23.jpg)
)400(0034.505.3ˆ y
![Page 24: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/24.jpg)
Prediction: Predict the fat gain for an individual whose NEA increases
by 400 cal by:
(a) using the graph ___________
(b) using the equation _________
2.2
145.2
![Page 25: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/25.jpg)
Predict the fat gain for an individual whose NEA increases by
1500 cal.
595.1ˆ)1500(0034.505.3ˆ
yy
![Page 26: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/26.jpg)
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
![Page 27: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/27.jpg)
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.
![Page 28: AP Statistics Section 3.2 A Regression Lines. Linear relationships between two quantitative variables are quite common. Correlation measures the direction.](https://reader036.fdocuments.us/reader036/viewer/2022062600/5a4d1b677f8b9ab0599b104e/html5/thumbnails/28.jpg)
ab