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Big Ideas Math Algebra 1, 2015

BI

Big Ideas Math Algebra 1, 2015 View details

5. Analyzing Lines of Fit

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Exercise 8 Page 206

Make a table of the residual values and then graph them on a scatter plot.

No, see solution.

Practice makes perfect

Let's begin by making a table of the residual values.

x	y	y=-0.5x-2	y-value From Model	Residual
4	-1	-0.5( 4)-2	-4	-1-(-4)= 3
6	-3	-0.5( 6)-2	-5	-3-(-5)= 2
8	-6	-0.5( 8)-2	-6	-6-(-6)= 0
10	-8	-0.5( 10)-2	-7	-8-(-7)= -1
12	-10	-0.5( 12)-2	-8	-10-(-8)= -2
14	-10	-0.5( 14)-2	-9	-10-(-9)= -1
16	-10	-0.5( 16)-2	-10	-10-(-10)= 0
18	-9	-0.5( 18)-2	-11	-9-(-11)= 2
20	-9	-0.5( 20)-2	-12	-9-(-12)= 3

Now we can create a scatter plot using the given x-values and our residuals. Remember, if the model is a good fit for the data, the scatter plot will be evenly distributed above and below the x-axis. Also, there will be no apparent patterns.

Scatter plot

This line of fit does not model the data well. It is not evenly distributed above and below the x-axis. We can see that the residual points form a U-shaped pattern, which suggests the data is not linear.

Subchapter links

Communicate Your Answer p.201

Monitoring Progress p.203-205