Question

Freight car loadings over an 18-week period at a busy port are as follows:

Week	Number	Week	Number	Week	Number
1	220	7	350	13	460
2	245	8	360	14	475
3	280	9	400	15	500
4	275	10	380	16	510
5	300	11	420	17	525
6	310	12	450	18	541

   
a. Determine a linear trend line for expected freight car loadings. (Round your intermediate calculations and final answers to 3 decimal places.)

I have determined the slope of 18.9959, but I don't know how to find the value of a at t=0.  

The equation will be Y = (a) + 19t.

Any help would be greatly appreciated.

Answer 1

Find t⋅Y and t² as it was done in the table below.

t	Y	t⋅Y	t.t
1	220	220	1
2	245	490	4
3	280	840	9
4	275	1100	16
5	300	1500	25
6	310	1860	36
7	350	2450	49
8	360	2880	64
9	400	3600	81
10	380	3800	100
11	420	4620	121
12	450	5400	144
13	460	5980	169
14	475	6650	196
15	500	7500	225
16	510	8160	256
17	525	8925	289
18	541	9738	324