if I test coefficient GDP, how do I know the degree of freedom = n-1 or n-1-k? if alpha in this case 10% , how do I know it is two tails or one tail test in order to look at the table 5% or 10%. thank you so much for your comments
sales =
10.2 +
(4.6 × CPI) +
(5.2 × IP) +
(11.7 × GDP)
(5.4)
(3.5)
(5.9)
(6.8)
A 90 percent confidence interval for the coefficient on GDP is:
A) –1.5 to 20.0. B) –1.9 to 19.6. C) 0.5 to 22.9.
Your answer: C was correct!
A 90% confidence interval with 176 degrees of freedom is coefficient ± tc (se ) = 11.7 ± 1.654 (6.8) or 0.5 to 22.9.
Always remember DF = n-k-1
The degrees of freedom in a multiple regression equals n-k-1 , where k is the number of variables.
For purposes of testing confidence interval there are some rules, it depends what kind of hypothesis one tests.
The rule of thumb is that
if the null hypothsis is that coeff is different from sth, then use two tails value
if the null is that coeff is larger/smaller then use one-tailed value
Note: When you use F-test, always one-tailed value.
I hope it is correct.
but i have one queastion too… is there any differences in number of degrees of freedom if the model is with intercept or without it ?
Pitmaster1:
The degrees of freedom in a multiple regression equals n-k-1 , where k is the number of variables.
For purposes of testing confidence interval there are some rules, it depends what kind of hypothesis one tests.
The rule of thumb is that
if the null hypothsis is that coeff is different from sth, then use two tails value
if the null is that coeff is larger/smaller then use one-tailed value
Note: When you use F-test, always one-tailed value.
I hope it is correct.
but i have one queastion too… is there any differences in number of degrees of freedom if the model is with intercept or without it ?
Like what you said, k = variables. An intercept is not a variable.
hey guys the 1 in n-k-1 is the intercept
k are independent variables,
need to subtract intercept (1) + number of variables (k) from observations (n) to get appropriate degrees of freedom.
this is why for a simple regression with one independent DF = n - 2, (1 for the intercept, 1 for the variable)
Dreary
May 12, 2012, 6:23pm
#7
Those two should be flipped.
No they should NOT be flipped. Pitmaster1 is correct.
Dreary
May 12, 2012, 11:27pm
#9
Flip them. This is getting confusing, hold on.
Dreary
May 12, 2012, 11:59pm
#10
The second one is correct, but the first one is a little confusing.
Example:
H0: x NOT= 10, so Ha: x=10, looks like a 1-tailed test to me.
H0: x =10, Ha: x > 10 or x < 10, that’s two tails for sure.
So, how can H0: x NOT= 10 be 2-tails, and the opposite of that, H0: x = 10 be also 2-tails?
Pitmaster1:
The degrees of freedom in a multiple regression equals n-k-1 , where k is the number of variables.
For purposes of testing confidence interval there are some rules, it depends what kind of hypothesis one tests.
The rule of thumb is that
if the null hypothsis is that coeff is different from sth, then use two tails value
if the null is that coeff is larger/smaller then use one-tailed value
Note: When you use F-test, always one-tailed value.
I hope it is correct.
but i have one queastion too… is there any differences in number of degrees of freedom if the model is with intercept or without it ?
I agree that both bullets under “rule of thumb” is correct. The first bullet is referring to a test like H0: b1 = 0. This would be a two-tailed test, because one way to test this is by obtaining a confidence interval. If the test stat falls out of either the lower bound or the upper bound, you reject the null. Therefore, it is a two-tailed test.
Dreary
May 13, 2012, 12:35am
#12
The first bullet says: if the null hypothsis is that coeff is different from sth, then use two tails value
So, it is not referring to a test like H0: b1 = 0, but more like a test like H0: b1 NOT= 0.
Anyway, I think it would still be a 2-tailed test, whether H0: b1 = 0 or H0: b1 NOT= 0.