Question

The following gives the number of accidents that occurred on Florida State Highway 101 during the last 4​ months:                                                                                                   Month Jan Feb Mar Apr Number of Accidents 25 45 70 105 Using the least-squares regressionLOADING... ​method, the trend equation for forecasting is ​(round your responses to two decimal ​places)​: ModifyingAbove y with caret ​= nothing ​+ nothingx

Answer 1

The Accident data

Month	Period (x)	Number of Accidents (y)	x*y	x^2
Jan	1	25	25	1
Feb	2	45	90	4
Mar	3	70	210	9
Apr	4	105	420	16
	10	245	745	30

We know that, using trend equation,

y = a + b*x

where y is number of accidents

x is the concerned period

a = {(∑y)*(∑x2) – (∑x)*(∑xy)} / {(n)*(∑x2) – (∑x)*(∑x)}

b = {(n)*(∑xy) – (∑x)*(∑y)} / {(n)*(∑x2) – (∑x)*(∑x)}

Here,

∑x = 10

∑y = 245

∑x*y = 745

∑x2 = 30

n = number of observations = 4

Putting all the values in a and b

a = {(245*30) – (10 * 745)}/{(4*30) – (10*10)}

= (7350 – 7450)/(120 – 100)

= -100/20

= -5

a = -5

b = {(4*745) – (10*245)}/{(4*30) – (10*10)}

= (2980 – 2450)/(120 – 100)

= 530/20

= 26.5

b = 26.5

Hence, y = 26.5*x – 5

Caret = 26.5*x – 5

.

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