Degree of freedom

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passcfaforsure

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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.
 
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 wrote:
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 ?
Click to expand...
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)
 
Pitmaster1 wrote:
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
Click to expand...
Those two should be flipped.
 
Pitmaster1 wrote:
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
Click to expand...
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
So, how can H0: x NOT= 10 be 2-tails, and the opposite of that, H0: x = 10 be also 2-tails?
 
Pitmaster1 wrote:
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 ?
Click to expand...
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.
 
skwak88 wrote:
I agree that both bullets under “rule of thumb” is correct. The first bullet is referring to a test like H0: b1 = 0.
Click to expand...
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.
 
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