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Cogito

Integrated Math 1 · Chapter 8 · Lesson 3

Practice Worksheet

Scatterplots and Lines of Fit

Fitting a line to real data.

12 problems · about 22 minutes · S-ID.B.6, S-ID.C.7

NameDate

Figure — use these to answer the problems

Adjust the line until it runs through the middle of the points, with roughly as many above as below.
-10-10-5-5551010
y = x + 1
Slope1
y-intercept1
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Predicted 30, actual 34. What is the residual?

    Answer

  2. What should a residual plot look like for a good linear model?

    • Random scatter with no leftover pattern.
    • A clear curve.

  3. y = 3x + 2 at x = 5. Predicted value?

    Answer

  4. Predicted 17, actual 14. Residual?

    Answer

  5. A negative residual means the model did what? 1 overestimated, 2 underestimated.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. A model has slope 4 dollars per hour. Predicted rise for 3 more hours, in dollars?

    Answer

  2. y = 0.5x + 10 at x = 20. Predicted value?

    Answer

  3. Does a good line of fit prove causation? 1 yes, 0 no.

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Put the fitting process in order.

    Write 1 to 4 in the boxes to put these in order.

    • Plot the data as a scatterplot.
    • Check whether the pattern looks linear.
    • Fit a line through the middle of the cloud.
    • Check the residuals for a leftover pattern.

  2. Predicted 25, actual 25. Residual?

    Answer

  3. The Residual

    Predicted 9, actual 11. What is the residual?

    Answer

  4. The Prediction

    y = 2x + 1 at x = 6. What is the predicted value?

    Answer