Problem Quants- Confidence Interval

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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)
28. 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?
 
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?
 
Onda wrote: thats what i am confused about. Why isnt it 35?
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How do you compute degrees of freedom?
Onda wrote: and why did they give us the T value if its useless?
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A better question is this: why didn’t you look up the correct t-value yourself?
 
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
 
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
 
Onda wrote: can you tell me what exactly i should be doing?
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No. I want you to discover that for yourself. It’ll be more useful to you that way.
Onda wrote: I get it that its degree of freedom, but why isnt it n-1 … ?
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What does the “1” in the formula n − 1 represent?
Onda wrote: … why were we given a t- value if its useless?
Click to expand...
Got me.
Onda wrote: am i looking at the one tail test
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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)
 
Onda wrote: I got it. The DF is n-k-1, so 34 is df …
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Yes: you’ve estimated two parameters, so you’ve lost two degrees of freedom.
Onda wrote: … and the t value associated with it 2.032 (at either 0.05 alpha or 0.025 alpha)
Click to expand...
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?
 
Onda wrote: DF=34 and alpha =0.025 equal to t=2.032
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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
 
Onda wrote: im terribly confused.
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We’ll fix that.
Onda wrote: But isnt it because its a two tail test?
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You keep using the word “test”. Why?
(As I mentioned before, look at the title you chose for this thread.)
Onda wrote: So the whole alpha is 5% …
Click to expand...
Yes.
Onda wrote: … but if we divide by two, each tail is 0.025
Click to expand...
But the area in each tail isn’t α, it’s … what?
 
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