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

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, , - 0.5, 0, 0.5, 0.75, or 1. a.b. Strong Negative Correlation r = Weak Positive Correlation r = 0.5

Checkpoint You complete 1 & 2 Use the following scale for “r” - 1, , - 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 y

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)

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) Groupx’sy’sMedian 11, __, 3__, 34, 40__ 25, 6, __35, 60, ____ 3__, 10, 1145, __, 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)

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 Group 1:(2, 34) Group 2:(6, 60) Group 3:(10, 50)

Checkpoint Find the equation of the median-median line

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