Problem Quants- Confidence Interval

CFA Level II Quant
#1

Question from the curriculum:

Selected Regression Output - Dependent Variable: Amtex Share Return Intercept 0.0095 ( coefficient ); 0.0078 ( standard error) Oil return 0.2354 ( coefficient ); 0.0760 ( standard error) ( Note: The critical t-value for a one-sided t-test at the 5% significance level is 1.691)

  1. Vasileva should compute the: A coefficient of determination to be 0.4689. B 95% confidence interval for the intercept to be –0.0037 to 0.0227. C 95% confidence interval for the slope coefficient to be 0.0810 to 0.3898.

The correct answer is C while I got B because I have used a df of 35 ( 36 total number of observations) and significance level of 5% ( t= 1.691 as shown above).

Thus, I did this for the confidence interval: 0.0095+ 1.691 ( 0.0078) = 0.22682 ( upper level) and 0.0095-1.691 (0.0078)= -0.003682 (lower level)

C is correct. The confidence interval for the slope coefficient is calculated as: Where b1 0.2354, sb1= 0.0760 and tc = 2.032

The lower limit for the confidence interval = 0.2354 – (2.032 × 0.0760) = 0.0810 The upper limit for the confidence interval = 0.2354 + (2.032 × 0.0760) = 0.3898

I don’t get it ; where is this 2.032 coming from and why are they not using 1.691 if it was given?

#2

How many observations?

What’s the confidence level or significance level for the confidence intervals?

#3

36 observations and 95% confidence level

#4

How many degrees of freedom do you have? (Hint: it isn’t 35.)

The note about the t-value is useless. Why?

#5

thats what i am confused about. Why isnt it 35? and why did they give us the T value if its useless?

#6

How do you compute degrees of freedom?

A better question is this: why didn’t you look up the correct t-value yourself?

#7

36-1=35

#8

what i am also confused on , is that they gave us the information of the t- value being 1.691 for one side test. So again I was confused if I should look at alpha =0.05 or alpha = 0.025

#9

Where did you get the “1”?

(Hint: it’s wrong.)

#10

n-1?

#11

No.

#12

can you tell me what exactly i should be doing? I get it that its degree of freedom, but why isnt it n-1 and second why were we given a t- value if its useless? am i looking at the one tail test

#13

No. I want you to discover that for yourself. It’ll be more useful to you that way.

What does the “1” in the formula n − 1 represent?

Got me.

What do you mean by “test”?

(Hint: look at the title you chose for this thread.)

#14

I got it. The DF is n-k-1, so 34 is df and the t value associated with it 2.032 (at either 0.05 alpha or 0.025 alpha)

#15

Yes: you’ve estimated two parameters, so you’ve lost two degrees of freedom.

It’s not the case that α = 0.05 or α = 0.025. It’s only one of those.

Which one?

How do you get t = 2.032?

Why?

#16

DF=34 and alpha =0.025 equal to t=2.032

#17

If C is correct, then α = 1 − confidence level = 1 − 95% = 5%, not 2.5%.

So, why is t = 2.032 correct? (It is, by the way.)

Note: you never did answer my question about “test”.

#18

im terribly confused.

But isnt it because its a two tail test? So the whole alpha is 5%, but if we divide by two , each tail is 0.025

#19

We’ll fix that.

You keep using the word “test”. Why?

(As I mentioned before, look at the title you chose for this thread.)

Yes.

But the area in each tail isn’t α, it’s . . . what?

#20

confidence interval is always a two tailed test