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Confidence interval for $ beta $ given only $hat{alpha}$ and $hat{beta}$ in linear regression
$begingroup$
Assuming that there is a correlation between the random variables X and Y, the line of regression was estimated based on 30 values $ (x_{i}, y_{i}) $(where 200 $leq$ x $leq$ 250 ) $:
$$ hat{y} = 6,206 + 0,029x $$
The question is if we can conclude that there is a correlation.
I know that we need to find the confidence interval for $ beta $
$$ ( hat{beta} - t_{n-2, a/2} s_{hat{beta}} , hat{beta} + t_{n-2,a/2}s_{hat{beta}} ) $$
and see if zero belongs to it.
But I think that we are not given enough data.
In what conclusions can we end up about the dependence of Y by X?
statistics linear-regression confidence-interval
asked Jan 26 at 20:30
Lena PappaLena Pappa
406
$endgroup$
add a comment |
$begingroup$
Assuming that there is a correlation between the random variables X and Y, the line of regression was estimated based on 30 values $ (x_{i}, y_{i}) $(where 200 $leq$ x $leq$ 250 ) $:
$$ hat{y} = 6,206 + 0,029x $$
The question is if we can conclude that there is a correlation.
I know that we need to find the confidence interval for $ beta $
$$ ( hat{beta} - t_{n-2, a/2} s_{hat{beta}} , hat{beta} + t_{n-2,a/2}s_{hat{beta}} ) $$
and see if zero belongs to it.
But I think that we are not given enough data.
In what conclusions can we end up about the dependence of Y by X?
statistics linear-regression confidence-interval
asked Jan 26 at 20:30
Lena PappaLena Pappa
406
$endgroup$
$begingroup$
From what you say, you certainly do need more information, such as the sample correlation or covariance between the $x_i$ and $y_i$ values, or the sample variances of each
$endgroup$
– Henry
Jan 26 at 21:56
add a comment |
$begingroup$
Assuming that there is a correlation between the random variables X and Y, the line of regression was estimated based on 30 values $ (x_{i}, y_{i}) $(where 200 $leq$ x $leq$ 250 ) $:
$$ hat{y} = 6,206 + 0,029x $$
The question is if we can conclude that there is a correlation.
I know that we need to find the confidence interval for $ beta $
$$ ( hat{beta} - t_{n-2, a/2} s_{hat{beta}} , hat{beta} + t_{n-2,a/2}s_{hat{beta}} ) $$
and see if zero belongs to it.
But I think that we are not given enough data.
In what conclusions can we end up about the dependence of Y by X?
statistics linear-regression confidence-interval
asked Jan 26 at 20:30
Lena PappaLena Pappa
406
$endgroup$
Assuming that there is a correlation between the random variables X and Y, the line of regression was estimated based on 30 values $ (x_{i}, y_{i}) $(where 200 $leq$ x $leq$ 250 ) $:
$$ hat{y} = 6,206 + 0,029x $$
The question is if we can conclude that there is a correlation.
I know that we need to find the confidence interval for $ beta $
$$ ( hat{beta} - t_{n-2, a/2} s_{hat{beta}} , hat{beta} + t_{n-2,a/2}s_{hat{beta}} ) $$
and see if zero belongs to it.
But I think that we are not given enough data.
In what conclusions can we end up about the dependence of Y by X?
statistics linear-regression confidence-interval
statistics linear-regression confidence-interval
asked Jan 26 at 20:30
Lena PappaLena Pappa
406
asked Jan 26 at 20:30
Lena PappaLena Pappa
406
edited Jan 26 at 20:39
Lena Pappa
asked Jan 26 at 20:30
Lena PappaLena Pappa
406
asked Jan 26 at 20:30
Lena PappaLena Pappa
406
asked Jan 26 at 20:30
Lena PappaLena Pappa
406
406
$begingroup$
From what you say, you certainly do need more information, such as the sample correlation or covariance between the $x_i$ and $y_i$ values, or the sample variances of each
$endgroup$
– Henry
Jan 26 at 21:56
add a comment |
$begingroup$
From what you say, you certainly do need more information, such as the sample correlation or covariance between the $x_i$ and $y_i$ values, or the sample variances of each
$endgroup$
– Henry
Jan 26 at 21:56
$begingroup$
From what you say, you certainly do need more information, such as the sample correlation or covariance between the $x_i$ and $y_i$ values, or the sample variances of each
$endgroup$
– Henry
Jan 26 at 21:56
$begingroup$
From what you say, you certainly do need more information, such as the sample correlation or covariance between the $x_i$ and $y_i$ values, or the sample variances of each
$endgroup$
– Henry
Jan 26 at 21:56
add a comment |
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$begingroup$
From what you say, you certainly do need more information, such as the sample correlation or covariance between the $x_i$ and $y_i$ values, or the sample variances of each
$endgroup$
– Henry
Jan 26 at 21:56