Section 4.2

Building Linear Models from Data

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OBJECTIVE 1

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(a) Draw a scatter diagram of the data, treating on-base percentage as the independent variable.

(b) Use a graphing utility to draw a scatter diagram.

(c) Describe what happens to runs scored as the on-base percentage increases.

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OBJECTIVE 2

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(a)Select two points and find an equation of the line containing the points.

(b) Graph the line on the scatter diagram obtained in the previous example.

(a) Using (34.7, 865) and (32.7, 691) m = 865 – 691 = 87 34.7 – 32.7

y = 87x + b 865 = 87(34.7) + b b = -2153.9

y = 87x – 2153.99

y = 87x – 2153.9

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OBJECTIVE 3

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(a) Use a graphing utility to find the line of best fit that models the relation between on-base percentage and runs scored.

(b) Graph the line of best fit on the scatter diagram obtained in the previous example.

(c) Interpret the slope.

(d) Use the line of best fit to predict the number of runs a team will score if their on-base percentage is 33.5.

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For the following data:

(a) Draw a scatter diagram.

(b) Select two points from the scatter diagram and find the equation of the line containing the points selected.

Using (7,3) and (9,6); m = 6 - 3 = 3/2. y = 3/2x + b 9 - 7

(7,3): 3 = 3/2(7) + b b = -15/2 y = 1.5x – 7.5

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x

y

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(c) Graph the line found in part (b) on the scatter diagram.

y = 1.5x – 7.5

(d) Use the calculator to find the line of best fit.

y = 1.13x – 3.86

(e) Using the best fit line found in (d) on the same scatter diagram

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