Students will be able to find a linear equation that approximates a set of data points. Warm-Up CD...

Students will be able to find a linear equation that approximates a set of data points.

Warm-UpCD SINGLES

The table shows the total number of CD single shipped (in millions) by manufacturers for several years during the period 1993–1997.

Create a scatter plot of the data.

Remember- x is the independent variable- y is the dependent variable


Homework Review


Quiz 5.1 – 5.4

• When you are done with the quiz do not hand it in. I will collect it when everyone is done.


Warm Up

• Write an equation in slope-intercept form of the line that passes through the points.

1. (5, 32), (7,16)

2. (0, 160), (25, 610)

3. (-12, -15), (-18, -12)

y = -8x + 72

y = 18x + 160

y = -1/2x - 21


Usually, there is no single line that passes through all the data points, so you try to find the line that best fits the data. This is called the best-fitting line.best-fitting line.

There are several ways to find the best-fitting line for a given set of data points. In this lesson, you will use a graphical approach.

–8

8

6

4

2

–2

–4

–6

0 2 4 6–2–4–6–8

FITTING A LINE TO DATA


DISCUS THROWS

Years since 1900

Dis

tanc

e (f

t)

0 8 16 24 32 40 48 56 64 72 80 88 96 104100

110

120

130

140

150

160

170

180

190

200

210

220

230

240

250

Write an equation of your line.

The winning Olympic discus throws from 1908 to 1996 are plotted in the graph. Approximate the best-fitting line for these throws.


Years since 1900

Dis

tanc

e (f

t)

0 8 16 24 32 40 48 56 64 72 80 88 96 104100

110

120

130

140

150

160

170

180

190

200

210

220

230

240

250

SOLUTION

Find two points that lie on the best-fitting line,

such as (8, 138) and

(96, 230).

Find the slope of the line through these points.

(96, 230).

(96, 230)

(8, 138)

(8, 138)


9288= 1.05

Years since 1900

Dis

tanc

e (f

t)

0 8 16 24 32 40 48 56 64 72 80 88 96 104100

110

120

130

140

150

160

170

180

190

200

210

220

230

240

250

(96, 230)

(8, 138)

y = m x + b

230 – 13896 – 8

=

129.6 = b

Write slope intercept form.

Substitute 1.05 for m, 8 for x, 138 for y.

Simplify.

Solve for b.

An equation of the best-fitting line is y = 1.05 x + 129.6.

138 = (1.05) (8) + b

y = m x + b

138 = 8.4 + b

y2 – y1

x2 – x1m =

In most years, the winner of the discus throw was able to throw the discus farther than the previous winner.

230 – 13896 – 8

= 9288

= 1.05


DETERMINING THE CORRELATION OF X AND Y

In this scatter plot, x and y have a positive correlation, which means that the points can be approximated by a line with a positive slope.



In this scatter plot, x and y have a negative correlation, which means that the points can be approximated by a line with a negative slope.



In this scatter plot, x and y have relatively no correlation, which means that the points cannot be approximated by a line.



TYPES OF CORRELATION

Positive Correlation No CorrelationNegative Correlation


Draw a scatter plot of the data. State the type of correlation that the data has. If possible, draw a line that closely fits the data and write an equation of the line.

1. 2. 3.X Y

1 2

2 9

3 8

4 1

5 4

6 8

X Y

-3 8

-2 6

-1 5

0 3

1 2

2 0

X Y

1.1 5.1

1.7 5.5

2.2 5.9

2.6 6.3

3.3 7.5

3.5 7.6

No Correlation Negative Correlation Positive Correlation y = -1.54x + 3.23 y = 1.10x + 3.68


Practice: workbook 5-4

Students will be able to find a linear equation that approximates a set of data points. Warm-Up CD...

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