The average asking rent for 10 markets, and the corresponding monthly mortgage on the median priced home (including taxes and insurance) for 10 cities are given in Rent ($)Mortgage ($)City 1840539City 210621002City 3823626City 4779711City 5796655City 61071977City 7953776City 8851695City 9762651City 10723654 What is the simple linear regression model to predict the monthly mortgage on the median priced home, using average asking rent? Fill in the coefficient for the LINEAR independent variable (keep 2 decimal points).

Answered: The average asking rent for 10 markets,…

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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Question

The average asking rent for 10 markets, and the corresponding monthly mortgage on the median priced home (including taxes and insurance) for 10 cities are given in

	Rent ($)	Mortgage ($)
City 1	840	539
City 2	1062	1002
City 3	823	626
City 4	779	711
City 5	796	655
City 6	1071	977
City 7	953	776
City 8	851	695
City 9	762	651
City 10	723	654

What is the simple linear regression model to predict the monthly mortgage on the median priced home, using average asking rent? Fill in the coefficient for the LINEAR independent variable (keep 2 decimal points).

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.

Expert Solution

Step 1

The given data is as follows,

The random variable $X$ is the rent

The random variable $Y$ is the mortgage

Rent	Mortgage
840	539
1062	1002
823	626
779	711
796	655
1071	977
953	776
851	695
762	651
723	654

The simple linear regression model is as follows,

$\hat{Y} = a + b X$

$Y$ is dependent variable

$X$ is independent variable

$a = \frac{\sum_{}^{} Y \sum_{}^{} X^{2} - \sum_{}^{} X \sum_{}^{} X Y}{n \sum_{}^{} X^{2} - {(\sum_{}^{} X)}^{2}} b = \frac{n \sum_{}^{} X Y - \sum_{}^{} X \sum_{}^{} Y}{n \sum_{}^{} X^{2} - {(\sum_{}^{} X)}^{2}}$