00:01
For this problem, i'll note that for the first part of the question, where we are trying to identify the correct time series, we don't really need to do all that much work to be able to figure out which one is appropriate.
00:12
What i'll do is just quickly sketch out what the time series would be for the first year, and then we can use that to recognize which plot corresponds.
00:22
So we can see that if we are considering the different quarters of year 1, we can see that first quarter year 1 we had 12, then second quarter we had 10, third quarter a value of 11, and fourth quarter a value of 13.
00:39
So we know that the first year portion should follow a pattern like this.
00:44
Out of all the options, the only one that matches that is going to be the fourth listed option.
00:54
Of course, if you're creating this by hand, well, all you really need to do is recognize that the data table is representing the different quarters as the rows, and the different years as the different columns.
01:07
So putting it together as a time series plot, what you need to do is basically read down the first column, then move over to the second, read down the second column, and so on when you're plotting out the data.
01:19
And what we can recognize as well is that looking at the data, we don't have something perfectly following this kind of pattern, but we roughly have something, we roughly have a pattern a little bit like this.
01:31
We basically have that same kind of repeating pattern going for each year.
01:38
Not exactly, but roughly.
01:40
So what that tells us is that there is both a linear trend as well as a yearly or seasonal pattern.
01:48
So regarding the type of pattern, we have linear trend, trending upwards, and a seasonal pattern.
02:06
And therefore that corresponds to the fourth listed option for the type of pattern that exists in the data.
02:26
Now for part b, i'll note that it does say a statistical program is suggested for this.
02:33
So for part b, what i'll do is jump over into excel.
02:40
Now for part b, we are asked to create the estimated regression equation to account for seasonal and linear trend effects in the data, where we have a bunch of different dummy variables to use.
02:52
So what i'll do is we'll first want to put all of the data into a single column.
03:00
So, or actually i shouldn't be cutting and pasting, i'll copy and paste.
03:05
Pardon me.
03:06
So as i said, first put all the data into a single column, where i'll have my y's there.
03:13
Then what we'll want to do is, there are three dummy variables, but then also we need to make sure that we include a variable for the actual time or time steps, since we want to make sure that we are accounting for any kind of linear trend as well.
03:29
So the different t values would just be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14, and 15, and 16.
03:42
And then we have our different dummy variables, x1, x2, x3.
03:47
Now we know that x1 is equal to 1 when it's quarter 1.
03:52
So we'll do 1, 0, 0, 0.
03:54
And then i'll just drag this down, so it creates a repeating pattern of 1, 0, oh, actually, no, it did not figure that out.
04:01
Okay...