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Solutions for Session 7: Homework
See solutions for Problems: H1 | H2 | H3 | H4 | H5 | H6
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Problem H1 | |
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Overall, there is a positive association between forearm length and foot length. On the graph, the points generally go up and to the right.
<< back to Problem H1
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Problem H2 | |
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To find the quadrants, we must use the mean forearm and foot lengths, which we know are 262.1 mm and 255.7 mm, respectively.
Recall that:
• | Quadrant I has points that correspond to people with above-average forearm and foot lengths. |
• | Quadrant II has points that correspond to people with below-average forearm lengths and above-average foot lengths. |
• | Quadrant III has points that correspond to people with below-average forearm and foot lengths. |
• | Quadrant IV has points that correspond to people with above-average forearm lengths and below-average foot lengths. |
Here is the scatter plot divided into quadrants:
This table shows which quadrant each point is in:
<< back to Problem H2
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Problem H3 | |
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a. | The contingency table is above. |
b. | Of the eight people with above-average forearm lengths, 87.5% (7 / 8) also have above-average foot lengths. |
c. | Of the eight people with above-average forearm lengths, only 12.5% (1/ 8) have below-average foot lengths. |
d. | Of the 12 people with below-average forearm lengths, 83.3% (10 / 12) also have below-average foot lengths. |
e. | Of the 11 people with below-average forearm lengths, only 16.7% (2 / 12) have above-average foot lengths. |
f. | These percentages say that there is a fairly strong (more than 80%) positive association between forearm length and foot length. |
<< back to Problem H3
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Problem H4 | |
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a. Here is the completed table:
b. The SSE, (256 + 324 + ... + 400 + 1), is 3,374.
<< back to Problem H4
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Problem H5 | |
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Here is the completed table:
b. The SSE, (400 + 196 +... + 576 + 25), is 4,558.
<< back to Problem H5
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Problem H6 | |
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The first SSE is smaller, which means that the line Foot Length = Forearm Length is a better fit to the data than the line Foot Length = Forearm Length + 4. Here is an illustration of these two lines on top of the data set:
As you can see from the graph, the line Foot Length = Forearm Length is a closer representation of the data than the line Foot Length = Forearm Length + 4.
<< back to Problem H6
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