Answered: The following gives the number of…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.6: Regression And Median-fit Lines

Problem 4GP

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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

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

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