00:01
For question number 14 about a, we want to get the least squares line equation, which is y equals mx plus b.
00:12
So we will need to get the m value, which is equal to n sigma xy minus sigma x by sigma y over n sigma square x squared minus sigma x squared.
00:36
And we will need to get the b value which is equal to sigma y minus m sigma x over n.
00:54
And we will need to get the r value.
00:59
So i will just write it here.
01:04
R value is equal to n sigma x y minus sigma x by sigma y over the square root of n sigma.
01:18
X square minus sigma x all squared multiplied by the square root of n sigma y squared minus sigma y all squared so here let's let's see what is given we have the years given and the consumer credit per billion dollars so what i did here is that i translated the year into an x value.
01:57
Since x is the year since year 2000, so at year 2000 we have x of 0.
02:05
At year 2001, we have x equal 1 and so on.
02:11
I then get all the needed elements, x squared, y squared, x, y, squared, x, y, the values, and the sum.
02:22
Of all values.
02:24
So now we can easily get the m value which would be equal to eight because we have n equals eight because we have eight years.
02:42
So m equals eight by 464 .3 minus 28 by 138 by 134.
03:06
0 .2 over 8 multiplied by 140 minus 28 all squared so that give us an m value of negative 0 .1286.
03:32
And surely we can get now the values the value of b which is equal to sigma y minus m by sigma x over n which is 8 in this case so we have an b value of 17 .225 and now we can get the least squares line equation which is y equals negative 0 .186 x plus 17 .286 x plus 17 .2 to five whereas y is the consumer credit in billion dollars and x is the year since year 2000 and we can also get the correlation coefficient r which is equal to 8 multiplied by 464 .3 minus sigma x by sigma x by sigma y so 28 by 133 so 28 by 134 0 .2 over the square root of 8 multiplied by sigma x square which is 140 minus 28 all squared multiplied by the square root of 800 by 2 ,252 .18 minus 134 .2 .18 minus 134 .2.
05:56
Squared so we will have an r value of negative 0 .849 and this is in part a now let's do the same for part b we will just exclude some years so as we can see here we have excluded excluded year 2001 in 2003 2004 2007 and we will do just the same process all over again so we'll get the m value for the new xy values and the corresponding x squared y squared and xy values so the new m value would be equal to only four m is four in this case n is equal to four four years so four multiplied by 200 point which is sigma x y minus 12 multiplied by 67 .5 which is sigma x by sigma y over n by sigma x squared which is 56 minus sigma x all squared which is 12 squared so we will have an m value of negative 0 .1...