In a simple linear regression you are told that the estimate of the slope coefficient was 0.9 and that the "t-statistic" for testing whether the slope parameter was unity or not was -3.8. What is the estimated standard error for the estimated slope coefficient?
20 out of 25 cars are red, with a past probability of 0.28?
To calculate the estimated standard error for the estimated slope coefficient in a simple linear regression, you would need two pieces of information: the estimate of the slope coefficient and the t-statistic.
The estimated standard error (SE) of the estimated slope coefficient can be calculated using the formula:
SE = estimated standard deviation / sqrt(sample size)
In this case, the estimated standard deviation is not given, but we can use the t-statistic and the degrees of freedom to calculate it.
The t-statistic is calculated by dividing the estimated slope coefficient by its standard error:
t = estimated slope coefficient / SE
Rearranging the formula, we can solve for the standard error:
SE = estimated slope coefficient / t
Plugging in the given numbers, the estimated slope coefficient is 0.9 and the t-statistic is -3.8:
SE = 0.9 / (-3.8)
Now we can calculate the estimated standard error:
SE ≈ -0.237
Therefore, the estimated standard error for the estimated slope coefficient is approximately -0.237.