The dau from exercise I follow Use equation 1423 to estimate

The dau from exercise I follow.  Use equation (14.23) to estimate the standard deviation of y* when x = 4.  Use expression (14.24) to develop a 95% confidence interval for the expected value of v when x = 4. Use equation (14.26) to estimate the standard deviation of an individual value of y when .r = 4.  Use expression (14.27) to develop a 95% prediction interval for y when x = 4.

Solution

regression equation: yi = 0.2 + 2.6*xi.....

when x=4 , y*-hat = 0.2 + ( 2.6*4) = 10.6...
a)s.d(y*-hat) = sqrt [ ( yi - y*-hat)^2 / (n-2) ] =  6.159004......

b) y when x=4 is 10.6..s.e = cov(x,y) * sqrt [ (1/n) + (x- x-bar)^2 / ss(x) ] = 2.848157...
95% confidence interval = [ 10.6 - ( 2.776445 * 2.848157) , 10.6 + ( 2.776445 * 2.848157) ]
= [ 2.69 , 18.51 ]

c) s.d ( y) = 6.159004 * sqrt(5) =13.77195....
d)
s.e of prediction interval =  cov(x,y) * sqrt [ 1 + (1/n) + (x- x-bar)^2 / ss(x) ]

= 5.928912....
t-score = 2.776445..
prediction interval = [ 10.6 - ( 2.776445 * 5.928912 ) , 10.6 + ( 2.776445 * 5.928912 ) ]
= [ -5.861298 , 27.0613 ]