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

wpe25.jpg (881 bytes)    x        y

wpe26.jpg (881 bytes)

    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.

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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.

 

 

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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.