00:01
Now is problem number 11 part a, we want to get the list the least squares line, which has equation of y equals mx plus b, whereas y is the number of u .s.
00:23
Banks in thousand, in thousand bank and the x is the year since year 1990.
00:35
So we need to get the value of m, which is equal to n sigma xy minus sigma x by sigma y over n sigma x squared minus sigma x all squared.
00:59
And we will need to get the value of b, which is equal to sigma y minus m multiplied by sigma x, over the value of n.
01:19
So we are given the value of sigma x to be 235 and sigma y has a value of 77 .564 and sigma x squared is equal to 5 ,605 .5.
01:58
Equals 603 .6324 and 634 and sigma xy is equal to 1810 .095 and the n value is equal to 10.
02:30
So we can say that m equals 10 10 by 1910 .095 minus 235 multiplied by 77 .56 over 10 by 5 ,605 minus 235 all squared.
03:26
So we will have a value of m equals negative 0 .153.
03:39
And the value of b equal to 77 .564 minus the m value, which is equal to negative 0 .1534, multiplied by sigma x64, minus the m value, which is equal to negative 0 .1534, multiplied by sigma x value of 234, all that over n which 10 by 5705 minus no sorry sorry so we divide for b value we divide by n which is equal to 10 so we have a b value of almost 11 .3611313 so the least squares line has the equation of y equals minus 0 .1534x plus 11 .3613.
05:17
So we have the equation for the number of banks in thousands for part b.
05:30
We want to know in year 2020.
05:43
We need to know the number of banks in year 2020.
05:50
So we will use an x value which is equal to 2020 minus 1990 because x is a value is a year since 1990.
06:08
So we will get a value of 30 and now we can get a value.
06:13
Get the value of number of banks, y, which is equal to negative 0 .15, 34, multiplied by x value, which is 30 years, plus 11 .3613.
06:41
So we will get the value of y equal to 6 .75.
06:43
So we will get the value of y equal to 6 .7 5993 ,000 banks...