Statistic HW - Requires mini tab
halaja
sta_282_hw_51.docxName________________
HW 5 (Chapter 4)
1. A pediatrician wants to determine the relation that may exist between a child’s height and head circumference. She randomly selects eleven 3-year-old children form her practice, measures their heights and head circumference, and obtains the data shown in the table.
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Height (inches) |
Head Circumference (inches) |
Height (inches) |
Head Circumference (inches) |
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27.75 |
17.5 |
26.5 |
17.3 |
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24.5 |
17.1 |
27 |
17.5 |
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25.5 |
17.1 |
26.75 |
17.3 |
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26 |
17.3 |
26.75 |
17.5 |
|
25 |
16.9 |
27.5 |
17.5 |
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27.75 |
17.6 |
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(a) If the pediatrician wants to use height to predict head circumference, determine which variable is the explanatory variable and which is the response variable
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Explanatory variable
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Response variable
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(b) Draw a scatter diagram in Minitab and insert it here.
(c) Find the linear correlation coefficient between the height and head circumference of a child.
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(d) Does a linear relation exist between height and head circumference? If so, describe the association. (i.e. strong negative, weak positive, etc.)
(e) Use Minitab to find the least-squares regression line. Use your answer in (a) to determine the explanatory variable, x, and response variable, y. Copy-and-paste your results here.
(f) Interpret the slope and y-intercept, if appropriate. If it is not appropriate to interpret the y-intercept, explain why.
(g) Use the regression equation to predict the head circumference of a child who is 25 inches tall. Compute the residual base on the observed head circumference of the child that is 25 inches tall in the table. Is the child above or below average?
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(h) Would it be reasonable to use the least-squares regression line to predict the head circumference of a child who was 32 inches tall? Why?
2. The time it takes for a planet to complete its orbit around the sun is called the planet’s sidereal year. In 1618, Johannes Kepler discovered that the sidereal year of a planet is related to the distance the planet is from the sun. The following data show that distances of the planets, and the dwarf planet Pluto, from the sun and their sidereal years.
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Planet |
Distance from Sun, x (millions of miles) |
Sidereal Year, y |
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Mercury |
36 |
0.24 |
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Venus |
67 |
0.62 |
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Earth |
93 |
1.00 |
|
Mars |
142 |
1.88 |
|
Jupiter |
483 |
11.9 |
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Saturn |
887 |
29.5 |
|
Uranus |
1785 |
84.0 |
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Neptune |
2797 |
165.0 |
|
Pluto |
3675 |
248.0 |
(a) Draw a scatter diagram of the data using Minitab and insert it here.
(b) Find the linear correlation coefficient between distance and sidereal year. Does this imply a linear relation between distance and sidereal year?
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(c) Find and interpret the coefficient of determination, R2.
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(d) Use Minitab to find the least-squares regression line. Insert your results here.
(e) Use Minitab to construct a plot of the residuals and insert it here. Do you think that a least-squares regression line is appropriate? Why?
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