7.1 7.1 Draw Scatter Plots & Draw Scatter Plots &

Best-Fitting LinesBest-Fitting Lines

7.1 HW Quiz: Friday7.1 HW Quiz: Friday7.1, 7.2 Quiz: TBA7.1, 7.2 Quiz: TBA

7.1, 7.2, 7.7 Test: Sept. 227.1, 7.2, 7.7 Test: Sept. 22

Make-up work

needs to be made

up by Monday

afternoon!Need: Graphing

Calculator

VocabularyVocabulary

Scatter plot:Scatter plot: a graph of a set of data pairs a graph of a set of data pairs (x, y)(x, y)

Positive correlation:Positive correlation: y tends y tends to increase as x increasesto increase as x increases

Negative correlation:Negative correlation: y tends y tends to decrease as x increasesto decrease as x increases

More VocabularyMore VocabularyCorrelation coefficient:Correlation coefficient: denoted by r, is denoted by r, is a number from -1 to 1 that measures how a number from -1 to 1 that measures how well a line fits a set of data pairs (x, y).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 If r is near 1, the points lie close to a line with a

positive slope.positive slope. If r is near -1, the points lie close to a line with a If r is near -1, the points lie close to a line with a

negative slope.negative slope. If r is near 0, the points do not lie close to any line. If r is near 0, the points do not lie close to any line.

Correlation Coefficient:Correlation Coefficient:

What do you think the correlation What do you think the correlation coefficient would be for these graphs?coefficient would be for these graphs?

x

y

x

y

x

y

x

y

x

y

If “r” is…If “r” is…

-.956-.956

.899.899

11

00

-1-1

0.50.5

-0.6-0.6

Guided Practice for Ex.1, p. 248Guided Practice for Ex.1, p. 248For each scatter plot, (a) tell whether the dataFor each scatter plot, (a) tell whether the data

have a positive, negative, or approximately have a positive, negative, or approximately no correlation, and (b) tell whether the no correlation, and (b) tell whether the correlation is closest to -1, -0.5, 0, 0.5, or 1. correlation is closest to -1, -0.5, 0, 0.5, or 1.

1)1) 2)2)

More VocabularyMore Vocabulary

Best-fitting line:Best-fitting line: line that lies as close as line that lies as close as possible to all the data pointspossible to all the data points

Linear regression:Linear regression: a method for finding a method for finding the equation of the best-fitting line, or the equation of the best-fitting line, or regression, which expresses the linear regression, which expresses the linear relationship between the independent relationship between the independent variable x and the dependent variable, y, variable x and the dependent variable, y, e.g. y = ax + b e.g. y = ax + b

Example 2: Example 2: Approximate the best-fitting lineApproximate the best-fitting line

ScatterplotScatterplot

Best-Fit Line EQBest-Fit Line EQ

Best-Fit Line GraphBest-Fit Line Graph

See Handout

Guided Practice for Example 2: p. 249Guided Practice for Example 2: p. 249

Draw a scatter plot and approximate the Draw a scatter plot and approximate the best-fitting line for the following data:best-fitting line for the following data:

(1, 22), (2, 30), (3, 33), (4, 39), (5, 45)(1, 22), (2, 30), (3, 33), (4, 39), (5, 45)

y = 5.5x + 17.3

Start Homework NOW!Start Homework NOW!

P. 250-251P. 250-251

#1-2, 7-9#1-2, 7-9

(may use graphing calculator)(may use graphing calculator)

Finish PSAT Practice WSFinish PSAT Practice WS

will turn in tomorrow!will turn in tomorrow!

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