00:01
For this problem, to begin, i'll note that since we have two independent variables, x1 and x2, we will have two regression degrees of freedom.
00:08
Since we have nine total degrees of freedom, that tells us that we must have seven residual degrees of freedom.
00:15
Then, we can use the fact that we know the regression sum of squares and the residual sum of squares, or the total sum of squares to find the residual.
00:23
Just do 1 .88 minus 1 .76209 to get that the residual sum of degrees of freedom.
00:35
Then, to find our mean squares, we take the ss values, we divide them by the number of degrees of freedom.
00:42
So, for the mean squares for regression, we would take 1 .76209, divide that by 2, giving us a result of 0 .881, roughly.
00:55
Similarly, for the residual sum of squares, 0 .1179 divided by 7, so that's about 0 .0168.
01:05
Then, our f score will be the regression sum of squares, 0 .881, divided by the residual sum of squares, 0 .0168, giving a result of 52 .44.
01:20
Now, i'll note for the regression statistics up above, one second here, our statists, pardon me, statistics, we have a few different things.
01:32
We'll be looking for the multiple r, the r square, the adjusted r square, the standard error, and the number of observations.
01:45
We can determine the number of observations now.
01:48
The total degrees of freedom will be number of observations minus 1, so we must have 10 observations.
01:53
The standard error is going to be the square root of the mean squares for the residual.
01:59
So, square root of 0 .0168 gives a result of 0 .1296.
02:07
And i believe we'll be able to calculate the rest, but the first thing that i'm going to turn my attention to here, or the next thing, is the significance f.
02:15
So, the significance f is going to be the f statistic for, let's see here, what level of significance are we testing at, 0 .05.
02:28
So, the f statistic for, i'll note this is 0 .05 to the right, and that should be 2 numerator degrees of freedom, 7 denominator degrees of freedom.
02:37
Now, i'm just going to use my software here to find this, though you could use something like excel, or there are plenty of online calculators.
02:43
So, i'm going to put in inverse cdf, f ratio distribution, to 7.
02:50
And if we want 0 .05 to the right, we want 0 .95 to the left.
02:54
So, we get, okay, wow, the significance f value here is roughly 4 .737.
03:00
So, we can see that at the alpha equals 0 .05 level of significance, well, our f score is greater than our critical value by a significant amount.
03:10
Therefore, we would reject the null hypothesis.
03:15
Now, i'll note that our multiple, or our, pardon me, our r squared value, unadjusted, is going to be equal to 1 minus the sum of squares for the residual, divided by the total sum of squares.
03:33
So, looking at our values here, we do 1 minus 0 .1179 over 1 .88, giving us a result of 0 .9373 as our r squared value.
03:50
I'll note that because we can see that the coefficients on both of our independent variables, beta 1 and beta 2, are greater than 0, that tells us that we are going to have a positive value for our r.
04:04
So, we'd be able to find our multiple r by taking the positive square root of r squared.
04:11
So, square root of 0 .9373 gives us a result of 0 .9681, 0 .9681...