correlation and median-median line statistics test: oct. 20 (wednesday)
DESCRIPTION
More Vocabulary Correlation coefficient: denoted by r, is a number from -1 to 1 that measures how well a line fits a set of data pairs (x, y). –If r is near 1, the points lie close to a line with a positive slope. –If r is near -1, the points lie close to a line with a negative slope. –If r is near 0, the points do not lie close to any line.TRANSCRIPT
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Correlation and
Median-Median Line
Statistics Test: Oct. 20 (Wednesday)
![Page 2: Correlation and Median-Median Line Statistics Test: Oct. 20 (Wednesday)](https://reader036.vdocuments.site/reader036/viewer/2022082409/5a4d1b4c7f8b9ab0599a5e15/html5/thumbnails/2.jpg)
Vocabulary• Scatter plot: a graph of a set of data pairs
(x, y)
• Positive correlation: y tends to increase as x increases
• Negative correlation: y tends to decrease as x increases
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More Vocabulary• Correlation coefficient: denoted by r, is
a number from -1 to 1 that measures how well a line fits a set of data pairs (x, y).– If r is near 1, the points lie close to a line with a
positive slope.– If r is near -1, the points lie close to a line with a
negative slope.– If r is near 0, the points do not lie close to any line.
![Page 4: Correlation and Median-Median Line Statistics Test: Oct. 20 (Wednesday)](https://reader036.vdocuments.site/reader036/viewer/2022082409/5a4d1b4c7f8b9ab0599a5e15/html5/thumbnails/4.jpg)
Correlation Coefficient:• What do you think the correlation
coefficient would be for these graphs?
x
y
x
y
x
y
x
y
x
y
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More Vocabulary• Best-fitting line: line that lies as close as
possible to all the data points• Linear regression: a method for finding
the equation of the best-fitting line, or regression, which expresses the linear relationship between the independent variable x and the dependent variable, y, e.g. y = ax + b
![Page 6: Correlation and Median-Median Line Statistics Test: Oct. 20 (Wednesday)](https://reader036.vdocuments.site/reader036/viewer/2022082409/5a4d1b4c7f8b9ab0599a5e15/html5/thumbnails/6.jpg)
Example 2: Approximate the best-fitting line
• Scatterplot• Best-Fit Line EQ
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Guided Practice for Example 2: p. 249
• Draw a scatter plot and approximate the best-fitting line for the following data:
(1, 22), (2, 30), (3, 33), (4, 39), (5, 45)
y = 5.5x + 17.3
![Page 8: Correlation and Median-Median Line Statistics Test: Oct. 20 (Wednesday)](https://reader036.vdocuments.site/reader036/viewer/2022082409/5a4d1b4c7f8b9ab0599a5e15/html5/thumbnails/8.jpg)
Finding the line of best-fitThere are several methods for finding “best-fit lines.”
We’re going to look at three of those methods:– Visually estimating – Linear-regression line – Median-median line
![Page 9: Correlation and Median-Median Line Statistics Test: Oct. 20 (Wednesday)](https://reader036.vdocuments.site/reader036/viewer/2022082409/5a4d1b4c7f8b9ab0599a5e15/html5/thumbnails/9.jpg)
Median-Median LineThis one’s a little more complicated.
Can you arrange these points in order by x-values from least to greatest?
(8, 26), (2, 15), (11, 32), (1, 15), (8, 23), (4, 18), (9, 27), (5, 21)
There’s MORE!
![Page 10: Correlation and Median-Median Line Statistics Test: Oct. 20 (Wednesday)](https://reader036.vdocuments.site/reader036/viewer/2022082409/5a4d1b4c7f8b9ab0599a5e15/html5/thumbnails/10.jpg)
(1,15)(2,15)(4,18)(5,21)(8,26)(8,23)(9,27)(11,32)
(1,15)(2,15)(4,18)(5,21)(8,23)(8,26)(9,27)(11,32)
Need to find the average to find
the median point
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Practice M-M-L’sUse the following data:(1, 22), (2, 27), (2, 20), (3, 15), (4, 19), (5, 10), (5,
14), (6, 9), (8, 7), (8, 11), (8, 13), (9, 5)
Answer: y = -2x + 24
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One more time!!(12,42), (15,72), (17,81), (11,95), (8,98), (14,78), (9,83), (13,87), (13,92)
(8,98)(9,83)(11,95)(12,42)(13,87)(13,92)(14,78)(15,72)(17,81)
Look at your
“y” values for
each
group….are
they in
order???
Answer: y = -2.83x + 121.58