 # Problem Quants- Confidence Interval

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?

How many observations?

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

36 observations and 95% confidence level

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

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

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

How do you compute degrees of freedom?

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

36-1=35

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

Where did you get the “1”?

(Hint: it’s wrong.)

n-1?

No.

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

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.)

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)

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?

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

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”.

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

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?

confidence interval is always a two tailed test