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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Income and housing revisited In Chapter 6, Exercise

32, we learned that the Office of Federal Housing Enter-
prise Oversight (OFHEO) collects data on various as-
pects of housing costs around the United States. Here’s a

scatterplot (by state) of the Housing Cost Index (HCI)
versus the Median Family Income (MFI) for the 50 states.
The correlation is r = 0.65. The mean HCI is 338.2,
with a standard deviation of 116.55. The mean MFI is
$46,234, with a standard deviation of $7072.47.a) Is a regression analysis appropriate? Explain.
b) What is the equation that predicts Housing Cost Index
from median family income?
c) For a state with MFI = +44,993, what would be the
predicted HCI?
d) Washington, DC, has an MFI of $44,993 and an HCI
of 548.02. How far off is the prediction in c) from the
actual HCI?
e) If we standardized both variables, what would be the
regression equation that predicts standardized HCI
from standardized MFI?
f) If we standardized both variables, what would be the
regression equation that predicts standardized MFI
from standardized HCI?

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Median Family Income
(thousands of dollars)
Housing Cost Index

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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