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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!
(show work!)(show work!)