00:01
The confidence interval for the beta or the slope.
00:03
So beta, we'll calculate beta first, which is given by n times sum of x y minus sum of x sum of y over n times sum of x squared minus sum of x squared.
00:25
So here n is the number of data points, so that's 15 and sum of xy is given as 1889 minus sum of x which is 252 sum of y 99 over 15 times x squared 4998 minus x squared sum of x squared 252 squared and and that brings to 0 .295.
01:12
And next, we'll calculate the standard error for the slope.
01:34
So, se, let's actually calculate the standard error of the estimate.
01:49
So, now, this is given by square root of 1 over n -2 times the rss, where rss is the residual sum of squares.
02:21
So to do this, we need to find alpha, and alpha or the intercept is given by sum of y minus beta sum of x over n.
02:36
And so sum of y was equal to 99 minus beta we found to be 0 .295 times sum of x 252 over 15 and okay so let's calculate this 1 .64 and now the rss is given by y sum of y minus y hat squared, where y hat is a prediction.
03:35
So now this is y squared minus 2 y y hat plus y hat squared, which is equal to sum of y squared minus 2 times sum of y y hat plus y sum of y hat squared.
04:20
And so now this is given by sum of y i squared is equal to 7 6 1 minus 2 times so you you would need to do this manually so um this is sum of y i times alpha plus alpha plus beta xi and you can use the data points in the problem.
05:04
And also this is alpha plus beta xi squared.
05:11
And now here alpha and beta was found above...