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Is there an association between the length of your forearm (elbow to wrist) and the length of your feet?

The following are measurements, in millimeters, for forearm length and right-foot length for 20 people:

N = 20 measurements

Mean forearm length = 262.1

Mean foot length = 255.7

**Scatter Plot**

**Problem H1
**Describe the association between forearm length and foot length.

**Problem H2
**Use the mean forearm length and the mean foot length to determine the quadrants and number of points in each quadrant.

**Problem H3
a. **Use the quadrants from Problem H2 to create the contingency table for this data.

b.

c.

d.

e.

f.

**Problem H4**

Consider the line Foot Length = Forearm Length (YL = X).

**a.** Complete the table below.

**b.** Determine the SSE for this data.

When you click “Show Answers,” the filled-in table will appear below the problem. Scroll down the page to see it.

**Problem H5
**Consider the line Foot Length = Forearm Length + 4 (YL = X + 4).

**Problem H6
**Compare the SSE in Problem H4 with the SSE in Problem H5. Which line provides a “better” fit? Explain.

**Problem H1**

Overall, there is a positive association between forearm length and foot length. On the graph, the points generally go up and to the right.

**Problem H2
**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:

**Problem H3**

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. |

**Problem H4:
**

**b.** The SSE, (256 + 324 + … + 400 + 1), is 3,374.

**Problem H5
a.** Here is the completed table:

**b. **The SSE, (400 + 196 +… + 576 + 25), is 4,558.

**Problem H6**

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.