00:01
So today we're going to make a 95 % confidence interval for beta 1.
00:08
And this is a coefficient of a multiple linear regression model.
00:13
So our model is as follows.
00:16
Y -hat is 1475 .28 minus 492 .84 x1 minus 273 .45 x2.
00:31
So this beta 1 coefficient is going to be this value right here.
00:35
This is a beta 1 coefficient.
00:38
Beta 1 is that.
00:40
And what we're testing is, we're essentially looking for this confidence interval to say whether or not this thing equals 0.
00:47
And that's essentially what this confidence interval is looking at.
00:50
And we're given, so we're given the coefficient.
00:53
And then we're also given, it's called the standard error.
00:56
So we'll put a little row down here.
00:57
This is our standard error row here.
01:00
And the standard error for this constant term is 243 .52.
01:07
And we're given the constant, or the standard error for this term is 127 .47.
01:14
I'll put parentheses around these so we don't get them confused with part of the equation.
01:18
And then the standard error for the second coefficient is 212 .06.
01:27
And we're given some t values and p values as well.
01:30
And then let's just look at this one for x2, that coefficient here, beta 1.
01:36
The t value was negative 3 .87.
01:38
And the p value that's associated with that was 0 .001.
01:44
So if we were testing the hypothesis that, the null hypothesis that, let me start that over.
01:51
The null hypothesis that beta 1 is equal to 0 against the alternative beta 1 is not equal to 0.
01:57
We could say, oh, the p value, oh, and we have an alpha of say 0 .05.
02:03
We would reject the null hypothesis here because the p value is less than this alpha.
02:08
So we can do that.
02:10
So now we're going to make a confidence interval for beta 1, which will kind of tell us the same thing, or will tell us the same thing.
02:16
So the confidence interval formula is as follows.
02:19
So we take our estimated beta 1, which is this, the negative 492 .84, plus minus t alpha over 2, note the degrees of freedom.
02:30
And then we multiply by the standard error of that estimated coefficient.
02:35
So like i said, we're given the standard error where we already know the coefficient...