Answered: The following gives the number of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Question

The following gives the number of accidents that occured on Floridaq State highway 101 during the last 4 months"

month jan feb mar apr

# of accidents 30 45 60 95

Using the least-squares regression method the trend equation for forecasting is (round your responses to two decimal places):

^Y=[__]+[___]X

Expert Solution

Step 1

Let the linear trend equation using the least-squares method be

Y = A + BX

where Y => No. of accidents

X => time in months

A => y-intercept

& B => Slope of linear trend line

Then we have the least-square regression estimates of A & B calculated from the given data as

Month	X	Y	(x - $\bar{x}$ )²	(x - $\bar{x}$ )(y - $\bar{y}$ )
January	1	30	2.25	41.25
February	2	45	0.25	6.25
March	3	60	0.25	1.25
April	4	95	2.25	56.25
Total	10	230	5	105

$\bar{x} = \frac{1}{n} \sum_{i} x_{i} = \frac{1}{4} \times 10 = 2.5 \bar{y} = \frac{1}{n} \sum_{i} y_{i} = \frac{1}{4} \times 230 = 57.5$

Then

$\hat{B} = \frac{\sum_{i} (x_{i} - \bar{x}) (y_{i} - \bar{y})}{\sum_{i} {(x_{i} - \bar{x})}^{2}} = \frac{105}{5} = 21 \hat{A} = \bar{y} - \hat{B} \bar{x} = 57.5 - 21 \times 2.5 = 5$

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Correlation, Regression, and Association$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions