Correlation and

Median-Median Line

Statistics Test: Oct. 20 (Wednesday)

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

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.

Correlation Coefficient:• What do you think the correlation

coefficient would be for these graphs?

x

y

x

y

x

y

x

y

x

y

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

Example 2: Approximate the best-fitting line

• Scatterplot• Best-Fit Line EQ

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

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

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!

(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

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

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