Algebra 1 Common Core Student Edition, Grade 8-9

Concept Byte

Use W ith Lesson 9 - 7

Analyzing

Residual Plots

Co m m o n Co r e St a t e St a n d a r d s

S-ID.B.6b Inform ally assess th e f i t o f a function by

p lo ttin g and analyzing residuals.

MP 5

Recall that in the Concept Byte Using Residuals in Chapter 5, you used a residual plot

to determine whether the best linear model is a good fit for the data. You can also use

residual plots to analyze the fit of other models.

Activity

Analyze the residual plot to determine whether the model is a good fit for the data.

X 0.3 0.7 1.0 1.8 2.3 3.6 4.6 5.9 7.3 8.7 9.0 11.3 13.5 14.7

y 0.6 0.5 0.5 0.7 1.0 2.2 3.8 6.4 10.1 14.4 15.5 25.1 36.1 42.9

Step 1 Using a graphing calculator, create a scatter plot of the data.

The data appear to be best modeled by either a quadratic function or an

exponential function. Find both functions and then analyze the residual

plots to determine which function is a better fit for the data.

Step 2 Perform a quadratic regression.

Press 2 5 9. Select CALC and QUADREG to find the model.

y = 0.22x2 - 0.28x + 0.55

Step 3 Plot the residuals.

Press 253E B 9 1- Turn on Plot 1 using Lx for the Xlist. Place the cursor to select

the Ylist. Press LIST (2nd STAT) and select RESID. Press £ 2 0 9 10 graph.

There is no apparent pattern in the residual plot.

Step 4 Check the exponential function.

1. Using a graphing calculator, perform an exponential regression. Press 2 5 9 •
   Select CALC and EXPREG.
   What is the exponential function that models the data?


2. Using a graphing calculator, plot the residuals.
   Does the residual plot appear to follow a pattern? Sketch the residual plot.


3. Using what you know about residual plots, which type of model best fits the data?
   Explain.

Ex e r c i se

4. By analyzing the residual plots, determine whether the data are best modeled by a
   quadratic, an exponential, or a linear function. Explain.

X 0.43 0.78 1.10 2.05 3.14 4.60 6.23 7.51

y 0.84 0.90 0.95 1.13 1.38 1.80 2.43 3.07

7.51 8.83 9.03 10.20 11.51

3.90 4.05 5.01 6.36

MAIHEMATICAL

PRACTICES

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