Confidence Intervals

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sparty419

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Can someone please explain whats going on here? Thanks...

1) Consider the following estimated regression equation:
ROEt = 0.23 - 1.50 CEt
The standard error of the coefficient is 0.40 and the number of observations is 32. The 95 percent confidence
interval for the slope coefficient, b1, is:
A) {0.683 < b1 < 2.317}.
B) {-2.317 < b1 < -0.683}.
C) {-2.300 < b1 < -0.700}.
D) {-3.542 < b1 < 0.542}.

Your answer: A was incorrect. The correct answer was B)
{-2.317 < b1 < -0.683}.
The confidence interval is -1.50 � 2.042 (0.40), or {-2.317 < b1 < -0.683}.


2) Consider the regression results from the regression of Y against X for 50 observations:
Y = 5.0 + 1.5 X
The standard error of the coefficient is 0.50 and the standard error of the forecast is 0.52. The 95 percent
confidence interval for the predicted value of Y if X is 10 is:
A) {18.980 < Y < 21.019}.
B) {19.480 < Y < 20.052}.
C) {19.500 < Y < 20.500}.
D) {18.954 < Y < 21.046}.

Your answer: A was incorrect. The correct answer was D)
{18.954 < Y < 21.046}.
The predicted value of Y is: Y = 5.0 + [1.5 (10)] = 5.0 + 15 = 20. The confidence interval is 20 � 2.011 (0.52) or {18.954 < Y <
21.046}.


What are standard error of the coefficient and standard error of the observations?
 
There is no such animla as the standard error of the observations. Estimators have standard errors; observations have standard deviations.
 
... could someone please clarify this for me, I seem to be cloudy on z or t right now.

If the sample size is > 30 can you use either z or t?... that is, even if the population variance is unknown, since the sample size is large, the sample is normal? CLT

For Q 2, the answer given of D (using t = 2.011) vs. A (using z = 1.96) tells me that we need to use t eventhough the sample size is > 30?

What did I miss/forget here? Thanks.
 
If you have a sample standard deviation in the denominator, you should genuflect at the altar of statistical orthodoxy and use a t-distribution. As you point out for df > 30 or so, t-values and z-values are about the same. As a practical matter, if your hypothesis test gives significance for z but not for t and your sample size is reasonable and you care about this, you are putting too much importance on your alpha. What's so magical about alpha = 0.05 anyway? R.A. Fisher - the greatest statistician of them all - once remarked "0.05 is no less arbitrary than any other choice" and that's why we use it.
 
Thank you. As always your input is helpful and appreciated.

In short, when creating a confidence interval and we have an unknown pop variance use a t-value.

I imagine that since the CFAI text spent a half page or so describing why for large samples either can be used and that as df increases the t dist approaches the z, that the choices wouldn't include both solutions and make you choose as they did here.

R.A Fisher is that Irving Fisher? I thought he was more of an economist? Monetarist that got hammered in the '29 crash? I am gonna have to google that one. That must be one of those things my brain has discarded to make room for important ethical standards scenarios.
 
HOLD ON A SECOND!

Is confidence interval for regression no longer in the level 1 exam?
 
As far as I know Irving Fisher and R.A. Fisher are not related. Today's trivia questions:

1) What statistical test studied in CFA curriculum is named for RA Fisher?
2) In what bible passage does Jesus make a joke about "Fisher"?
3) Who was the greatest chess champion of all time?
 
Well now you did it, I had to Wiki these two because it is more fun than work.

Irving : quantity theory of money: MV=PT, real and nominal interest rates: r = (1 + i) / (1 + inflation) &#8722; 1 ; and the relation between unemployment and inflation known as the Phillips Curve, 30 years before Phillips. [I hereby declare it the 'Fisher Curve']

Ronald: analysis of variance, work on the z, t, F, and Chi distributions (I am guessing the F test is named for him), non-parametric tests, then a slew of genetical theory / natural selection.

pretty sad that I can't quickly recall that these were two different people.

As for Robert, he is best known as a nut-job, a conspiracy theorist and for making inflamatory statements, both anti-american and anti-semitic.
 
Does that mean we won't be getting any questions like the one I posted?
 
JoeyDVivre Wrote:
-------------------------------------------------------
> As far as I know Irving Fisher and R.A. Fisher are
> not related. Today's trivia questions:
>
> 1) What statistical test studied in CFA curriculum
> is named for RA Fisher?
> 2) In what bible passage does Jesus make a joke
> about "Fisher"?
> 3) Who was the greatest chess champion of all
> time?



excuse my ignorance of western surnames, but are Fisher and Fischer used interchangeably?
 
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