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

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

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”

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

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

Checkpoint• You complete 1 & 2

• Use the following scale for “r”

• - 1, - 0.75, - 0.5, 1, 0.5, 0.75, 1

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

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

Checkpoint • Use the table to answer the questions

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)

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: (__, __)

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

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)

Checkpoint• Find the equation of the median-median line

4 18y x

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)

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

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

Homework

NTG pg. 260, 1 – 13 all

Homework

NTG pg. 260, 1 – 13 all