Grade Level: 9
This lesson will be
done in three sections. One section is lecture, another section is for
cooperative learning, and the third is for connections activity.
Aim: To find the line of best fit for a set of
data and to find the correlation coefficient for a set of data.
Standards:
Students will be able to…………
1.
Interpret
representations of data, compare distributions of data and critique
conclusions.
2.
Use technology to
represent and analyze functions and their graphs.
Do Now:
Given the slope of a line m=3 and given the y intercept y=5 find the equation
of that line.
Given the following table write the equation of the line
x
y
1 2
2 5
3 8
4 11
5 14
Given the following data find the
mean, median and mode:
5, 7, 6, 3,
8, 6, 4, 6, 4,
6, 4
Motivation: A great
student in Algebra 1, John, learned how to make predictions from a set of data
or from a given equation. John goes
home one night and tells his dad that he can help him to find the best price for
a used car. His dad is really upset because the Car Magazine doesn’t have the
year of the car that is looking for: TOYOTA/89
Model / Year |
Price (In Thousands) |
Toyota/87 |
2 |
Toyota/87 |
3 |
Toyota/88 |
3.5 |
Toyota/88 |
3 |
Toyota/90 |
5 |
Toyota/90 |
4.7 |
Toyota/92 |
5 |
When John saw this table he told
his dad that he could find out what the price would be for the year that is
missing. He plots the points and
TOYOTA GRAPH (MS WORD DOC.)
Now the question is what went
wrong?
Prior Knowledge:
Mean, Mode and Median.
Write the equation of a line
knowing slope y intercept, or just graph, table.
Standard Deviation, Scatter Diagram
Pivotal Questions:
1.
How many lines go through the cluster of data points?
(A lot.)
2.
Since it is impossible to draw a line
that touches every point, what is the best way to draw a line through those
points? (A line that is close enough to all the points)
3.
By hand try to draw a line that is really close to all
those points on the graph.
——————————————————————————————————————————————————
Practice:
1. Given the following data
x 1
1 2 4
y 1
2 2 6
Find
the line that best fits the data.
1.
Given the following data:
x 1
2 3 4 5 6
y 5
5 4 2 1 0
Find
the line that Best Fits the data and find the correlation coefficient.
3. Give the following Linear Equation
Line
A y= 1.5 + 0.5x
Line
B y= 1.125 + 0.375x
Data
Points
x 1
1 5 5
y 1
3 2 4
Determine
which line fits the set of data better.
4.
For the data above find your Best Fit Line and the
Correlation Coefficient.
5.
From the following data
x
(years) 6 6 6 6
7 4 3 5
y
(Price) 12 15 12 23 18 9 19
16
Find
the Correlation Coefficient and the equation of the line that best fits this
data.
————————————————————————————————————————————————————————
Homework:
1. Give the following Lines and data,
determine which line is better according to the data below.
Line A y= 3 -
0.6x
Line B y= 4 - x
x 0 2 2 5
6
y 4
2 0 -2 1
2. A random sample of 11 males age 18-24
years gave the following data, where x denotes height, in inches, and y denotes
weight, in pounds.
X 65
67 71 71 66 75 67 70 71 69 69
Y 175
133 185 163
126 198 153
163 159 151
155
Find the
correlation Coefficient.
Find the line
that best fits the data.