Cute little pluggy chuggy problem … shouldn’t be any problem if you have the formula sheet handy. A variable y is regressed against a single variable x across 28 observations. The value of the slope is 1.89, and the constant is 1.1. The mean value of x is 1.50, and the mean value of y is 3.94. The standard deviation of the x variable is 0.96, and the standard deviation of the y variable is 2.85. The regression sum of squares is 79.07, and the total sum of squares is 195.24. For an x value of 2.0, what is the 95% confidence interval for the y value? A) 1.01 to 8.75. B) 1.21 to 8.65. C) 1.50 to 8.36. D) 0.41 to 9.35.
D (but I can’t figure the rounding error) n got me kinda messed up. since it is less than 30, i first went with a z-score, but none of the answers worked, so i went with the t critical value of 2.056 that i found via wiki. just gotta remember that TSS - RSS = SSE and SEE = (SSE/n-2)^.5 then Sf^2= SEE^2(1 + 1/n + (Xi - AvgX)^2/(n-1)(Sx^2)) = 4.6725 Sf = 2.1616 tcrit = 2.056 1.1 + 1.89(2) = 4.88 4.88 ± 2.056(2.1616) => .44 to 9.32
I think tcrit is actually 2.048 which gives slightly more rounding error. Hmm. Good job though.
I got one right! Using the Maratikus Nasty Hack™ you do: SSE = 195.24 - 79.07 = 116.17 df = 26 so MSR = 116.17/26 = 4.47 standard error of estimate = SEE = MSR ^.5 = 4.47^.5 = 2.114 Estimated y value = y_hat = 1.1+1.89*2 = 4.88 t_26,2.5% = 2.0555 prediction interval is wider than: 4.88+/- 2.0555*2.114. so prediction interval is wider than (0.53,9.225), which leaves d) Doesn’t it feel nice to be dirty?
Joey…why use 28 dof? Why not 26? 28 observations and two parameters estimated…
Because Joey made a whoopsie.
isn’t this one of those horrible formulae where schweser says you are almost certain not to have to know it… i certainly hope so… i presume though from schweser’s wording that it is technically in the LOS…
Again, use the Maratikus Nasty Hack™. If they screw you, they screw you.
chrismaths Wrote: ------------------------------------------------------- > Again, use the Maratikus Nasty Hack™. If they > screw you, they screw you. that’s basically my mantra too… just my luck, they’ll have a huge question just based on the formula.
Brilliant guys!! ‘D’ is indeed the correct answer
Is there an easy way? schweser’s style for this kind of Q is to get the answer without calculation. How about we approximate sf = SEE = 2 & t=2 so the lower limit (at least)= 4.88-sf*t =4.88-4=0.88. Answer A,B,C fail the limit. Just for fun, guys.
So a bit like this then? Give it its proper name: the Maratikus Nasty Hack™ 
How do you know that the t stat is at least 2 without a table? We know it is larger than a normal distribution (1.96) but that’s all. We’d also be given a t table, so it’s not as if it’s extra work to look up the value. chrismaths Wrote: ------------------------------------------------------- > I got one right! > > Using the Maratikus Nasty Hack™ you do: > > SSE = 195.24 - 79.07 = 116.17 > df = 26 so > MSR = 116.17/26 = 4.47 > standard error of estimate = SEE = MSR ^.5 = > 4.47^.5 = 2.114 > Estimated y value = y_hat = 1.1+1.89*2 = 4.88 > t_26,2.5% = 2.0555 > > prediction interval is wider than: 4.88+/- > 2.0555*2.114. > > so prediction interval is wider than (0.53,9.225), > which leaves d) > > Doesn’t it feel nice to be dirty?
You are right, Christmath. But it makes me feel that I stole your idea. chrismaths Wrote: ------------------------------------------------------- > So a bit like this then? Give it its proper name: > the Maratikus Nasty Hack™ > > How do you know that the t stat is at least 2 > without a table? We know it is larger than a > normal distribution (1.96) but that’s all. We’d > also be given a t table, so it’s not as if it’s > extra work to look up the value. > > chrismaths Wrote: > -------------------------------------------------- > ----- > > I got one right! > > > > Using the Maratikus Nasty Hack™ you do: > > > > SSE = 195.24 - 79.07 = 116.17 > > df = 26 so > > MSR = 116.17/26 = 4.47 > > standard error of estimate = SEE = MSR ^.5 = > > 4.47^.5 = 2.114 > > Estimated y value = y_hat = 1.1+1.89*2 = 4.88 > > t_26,2.5% = 2.0555 > > > > prediction interval is wider than: 4.88+/- > > 2.0555*2.114. > > > > so prediction interval is wider than > (0.53,9.225), > > which leaves d) > > > > Doesn’t it feel nice to be dirty?