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