7.1 draw scatter plots and best fitting lines pg. 255 notetaking guide pg. 255 notetaking guide

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7.1 Draw Scatter Plots and Best Fitting Lines Pg. 255 Notetaking Guide

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Page 1: 7.1 Draw Scatter Plots and Best Fitting Lines Pg. 255 Notetaking Guide Pg. 255 Notetaking Guide

7.1 Draw Scatter Plots and Best Fitting

Lines

7.1 Draw Scatter Plots and Best Fitting

Lines

Pg. 255Notetaking Guide

Pg. 255Notetaking Guide

Page 2: 7.1 Draw Scatter Plots and Best Fitting Lines Pg. 255 Notetaking Guide Pg. 255 Notetaking Guide

Vocabulary

• Scatter Plot– A graph of a set of data pairs (x, y)

• Positive Correlation– The relationship between paired data

when “y” tends to increase as “x” increases

• Negative Correlation– The relationship between paired data

when “y” tends to decrease as “x” increases

Page 3: 7.1 Draw Scatter Plots and Best Fitting Lines Pg. 255 Notetaking Guide Pg. 255 Notetaking Guide

Vocabulary (cont.)• Correlation Coefficient

– A number, denoted by “r”, from - 1 to 1 that measures how well a line fits a set of data pairs (x, y)

• Best Fitting Line– The line that lies as close as possible to all the date

points

• Linear Regression– A method for finding the equation of the best

fitting line, or regression line, which expresses the linear relationship between the independent variable “x” and the dependent variable “y”

Page 4: 7.1 Draw Scatter Plots and Best Fitting Lines Pg. 255 Notetaking Guide Pg. 255 Notetaking Guide

Vocabulary (cont.)• Median-Median Line

– A median-median line is a linear model used to fit a line to a data set. The line is fit only to summary points, “key” points calculated using medians.

• Algebraic Model– An expression, equation, or function that represents data

or a real-world situation

• Inference– A logical conclusion that is derived from know data

Page 5: 7.1 Draw Scatter Plots and Best Fitting Lines Pg. 255 Notetaking Guide Pg. 255 Notetaking Guide

Example #1 (Correlation Coefficients)

• Describe the data as having a positive correlation, a negative correlation, or approximately no correlation. Tell whether the correlation coefficient for the data is closest to – 1, - 0.75, - 0.5, 0, 0.5, 0.75, or 1.

• a. b.

Strong Negative Correlationr = - 0.75

Weak Positive Correlationr = 0.5

Page 6: 7.1 Draw Scatter Plots and Best Fitting Lines Pg. 255 Notetaking Guide Pg. 255 Notetaking Guide

Checkpoint• You complete 1 & 2

• Use the following scale for “r”

• - 1, - 0.75, - 0.5, 1, 0.5, 0.75, 1

Page 7: 7.1 Draw Scatter Plots and Best Fitting Lines Pg. 255 Notetaking Guide Pg. 255 Notetaking Guide

Example #2 (Best-Fitting Line)

• Approximate the best fitting line

• Draw a _____________• Sketch the best fitting line• Choose two points on the

scatter plot. {(1, 722), and (2, 750)}

• Write an equation of the line. We need the slope and y-intercept

x 1 2 3 4 5 6 7

y 722 763 772 826 815 857 897

Page 8: 7.1 Draw Scatter Plots and Best Fitting Lines Pg. 255 Notetaking Guide Pg. 255 Notetaking Guide

Example #2 (cont.)• Slope

• Now use the point-slope formula with one of your points

• (Only use one of your points (1, 722), & m = 28)

change in y

change in x

y risem

x run

750 722

282 1

m

1 1y y m x x

1

2

1,722

2,750

P

P

722 28 1y x

Page 9: 7.1 Draw Scatter Plots and Best Fitting Lines Pg. 255 Notetaking Guide Pg. 255 Notetaking Guide

Checkpoint • Use the table to answer the questions

Page 10: 7.1 Draw Scatter Plots and Best Fitting Lines Pg. 255 Notetaking Guide Pg. 255 Notetaking Guide

Example #3 (Median-Median Line)

• Find the equation for the median-median line• ** Make sure your data is in order from least to

greatest values “by the x values”• Divide data into 3 equal

size groups (if not possible make the first and last groups equal size and the center group smaller)

Page 11: 7.1 Draw Scatter Plots and Best Fitting Lines Pg. 255 Notetaking Guide Pg. 255 Notetaking Guide

Example #3 (cont.)

• Create a table of your values

• Create a summary point for each group (these are your x and y medians)

Group x’s y’s Median

Median

1 1, __, 3 __, 34, 40 __ __

2 5, 6, __ 35, 60, __ __ __

3 __, 10, 11

45, __, 60 __ __

Group 1: (__, __)

Group 2: (__, __)

Group 3: (__, __)

Page 12: 7.1 Draw Scatter Plots and Best Fitting Lines Pg. 255 Notetaking Guide Pg. 255 Notetaking Guide

Example #3 (cont.)

• Determine the equation of the line between the two outer (group 1 and group 3) summary points by finding the slope between the two points and then using the slope and one point in the point slope formula

Group 1: (2, 34)

Group 2: (6, 60)

Group 3: (10, 50)

m 1 1y y m x x

Page 13: 7.1 Draw Scatter Plots and Best Fitting Lines Pg. 255 Notetaking Guide Pg. 255 Notetaking Guide

Example #3 (cont.)• Final Step

– Move the equation from group 1 and group 3 one-third of the way to the middle summary point

• Middle summary point (6, 60)

• Use equation from group 1 and group 3 to find the predicted value for x = 6

• One third of the difference between y = 60 and y = 42

• Add the difference to the equation

2 30y x

62 30y x 2 36y x

Group 1: (2, 34)

Group 2: (6, 60)

Group 3: (10, 50)

Page 14: 7.1 Draw Scatter Plots and Best Fitting Lines Pg. 255 Notetaking Guide Pg. 255 Notetaking Guide

Checkpoint• Find the equation of the median-median line

4 18y x

Page 15: 7.1 Draw Scatter Plots and Best Fitting Lines Pg. 255 Notetaking Guide Pg. 255 Notetaking Guide

Practice (median-median)• (1, 22), (2, 27), (2, 20), (3, 15), (4, 19), (5, 10),

(5, 14), (6, 9), (8, 7), (8, 11), (8, 13), (9, 5)

Page 16: 7.1 Draw Scatter Plots and Best Fitting Lines Pg. 255 Notetaking Guide Pg. 255 Notetaking Guide

Practice (median-median)• (12, 42), (15, 72), (17, 81), (11, 95), (8, 98), (14,

78), (9, 83), (13, 87), (13, 92)

Page 17: 7.1 Draw Scatter Plots and Best Fitting Lines Pg. 255 Notetaking Guide Pg. 255 Notetaking Guide

Homework

NTG pg. 260, 1 – 13 all

Homework

NTG pg. 260, 1 – 13 all