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

Finding the line of best-fit There 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 Line This 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’s Use 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