Creating linear models for data

Student:
Class:
Date:
Creating linear models for data
Student Activity Sheet 5; use with Exploring “Line of best fit”
1. Here are two sample trend lines modeling the relationship between height and shoe size.
Which one do you think fits better? Why do you think so?
2. Create a scatterplot on your calculator and use the Linear Regression feature to find the
line of best fit. Record the information on your calculator screen, then use that
information to write the regression equation. Round to the hundredths place if
necessary.
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
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Student:
Class:
Date:
Creating linear models for data
Student Activity Sheet 5; use with Exploring “Line of best fit”
3. Now write your equation in context, replacing the variables with the labels.
4. Describe the correlation between height and shoe size. This is related to the r-value
shown on your calculator screen.
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
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With space for student work
Student:
Class:
Date:
Creating linear models for data
Student Activity Sheet 5; use with Exploring “Line of best fit”
5. Your calculator showed an r-value that is close to 1. What does an r-value close to 1
indicate? What would an r-value close to -1 indicate? What would an r-value close to 0
indicate?
6. Match the r-values with their graphs.
r = 0.33
r = -0.60
r = 0.87
7. Use the trend line equation y = 0.35x – 14 to answer the following questions.
a. Find a prediction for the shoe size of a boy who is 67” tall.
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
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Student:
Class:
Date:
Creating linear models for data
Student Activity Sheet 5; use with Exploring “Line of best fit”
b. In Coach Guerrero’s class, there actually was a boy 67” tall. Did the equation predict
the correct shoe size for that boy? If not, was the prediction an overestimate or an
underestimate?
8. Now use the equation to find a prediction for someone your height. Did the equation
correctly predict your shoe size? If not, was the prediction an overestimate or an
underestimate?
9. Locate the point on the graph that represents the 67” tall boy. Draw a vertical line from
the point to the trend line. Do the same for the remaining points. What do you notice
about the number and location of overestimates and underestimates?
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 4 of 6
With space for student work
Student:
Class:
Date:
Creating linear models for data
Student Activity Sheet 5; use with Exploring “Line of best fit”
10. Here are three trend lines of the (height, shoe size) data. Based on the error, illustrated
by the area of the error-squares, which of these is the best model for the data?
11. Look at the regression equation you found in question 3. Use this equation to determine
the predicted shoe size for each student in Coach Guerrero’s class. Then find the
residual (the overestimate or underestimate) for each point.
Height in
inches
62
74
70
67
53
58
Actual
Shoe Size
6
13
9
11
4
7
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Predicted Shoe Size
0.39(62)-16.56 = 7.6
Residual =
Actual – Predicted
6 – 7.6 = -1.6
Page 5 of 6
With space for student work
Student:
Class:
Date:
Creating linear models for data
Student Activity Sheet 5; use with Exploring “Line of best fit”
12. Complete the residual plot for these data by plotting the residual value for each
corresponding student height.
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
Page 6 of 6
With space for student work