Question

The following gives the number of accidents that occurred on Florida State Highway 101 during the last 4​ months:                                                                                                  

Month/Number of accidents

Jan 25

Feb 40

Mar 64

Apr 90

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

Answer 1

Solution:

From the data, it can be observed that there is an increasing trend in the number of accidents per month. and here the number of the accident is the dependent variable which depends on the month.

Let, the month be denoted by "x" i.e. x=1 for January, x= 2 for February and so on, and the number of accidents is represented by y, and the number of period is represented by n which is 4 here.

So, As per least regression model, the equation will be

y=a+b*x

and

where are the mean of x and y respectively.

The calculation for the above data is given in the following table

	x	y	x*y	x^2
	1	25	25	1
	2	40	80	4
	3	64	192	9
	4	90	360	16
Σ	10	219	657	30
Mean	2.5	54.75

Using the formula we can get,

b=21.9

and a=0

So, the trend equation as per lest square regression method is y=0+21.9*x i.e. y=21.9*x