00:01
Hey there, welcome to numerate.
00:03
So we are given our sample correlation coefficient here, and we're asked to find the slope and the y intercept of the least squares regression equation.
00:13
So let us find the slope first.
00:16
We get to know our slope as b.
00:18
B equals our correlation coefficient, multiplied by our standard deviation of y divided by the standard deviation of x, so therefore we plug in our values to solve for b, b equals 0 .801 for our correlation coefficient.
00:44
And i'm looking at this problem here and there is no data attached, so i went ahead and found a similar problem online, so hopefully the data matches.
00:54
But the standard deviation for sample y is around 9 .45, divided by the standard deviation for sample y is around 9 .45, divided by the standard deviation of sample x which is around 25 .25.
01:18
We calculate this and we get a slope rounded to two decimal places of around let us do 0 .2998 which rounds to 0 .23.
01:42
I mean sorry not two three three zero okay and then now we can plug this back into our equation here so we have our y minus our y mean equals our slope times x minus our x meet therefore we have our y mean as 28 .97 equals our slope so let's carry all the digits for this calculation to 99 times x minus the mean which is around the mean of x is 66 .09 now we're going to simplify this so just multiply in and then move into the right so we have 28 .97 equals 0 .298x minus we multiply that that will equal around 19 .82 and we move 20 .97 to the right right inside, giving us a slope of 2998x plus our intercept value of around around let's see what we get, 9 .918 1538...