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 -3.6. What is the estimated standard error for the estimated slope coefficient?
i have this very question. the answer is 0.69
To find the estimated standard error for the estimated slope coefficient in a simple linear regression, we can use the formula:
Standard Error = square root of [(sum of squared residuals) / (n - 2)] / (square root of sum of squared differences of X values from their mean)
However, we are not given the sum of squared residuals or the sum of squared differences of X values from their mean. Instead, we are told that the "t-statistic" for testing whether the slope parameter was unity or not was -3.6.
The t-statistic is given by the formula:
t = (estimated slope coefficient - hypothesized slope coefficient) / estimated standard error
In this case, the hypothesized slope coefficient is unity (i.e., 1). Therefore, we can rearrange the t-statistic formula to solve for the estimated standard error:
estimated standard error = (estimated slope coefficient - hypothesized slope coefficient) / t
Substituting the given values:
estimated standard error = (0.9 - 1) / (-3.6)
estimated standard error = -0.1 / (-3.6)
estimated standard error = 0.0278
Therefore, the estimated standard error for the estimated slope coefficient is approximately 0.0278.
To find the estimated standard error for the estimated slope coefficient in a simple linear regression, we can use the formula:
Standard Error = sqrt((Sum of Residual Squares) / (Degrees of Freedom))
The degrees of freedom in a simple linear regression are given by (n - 2), where n is the number of observations.
In this case, we have been given that the estimate of the slope coefficient is 0.9 and the t-statistic for testing whether the slope parameter is unity or not is -3.6.
The t-statistic can be calculated using the formula:
t = (Estimated slope coefficient - Hypothesized slope coefficient) / (Standard Error)
We are testing whether the slope parameter is unity or not (1 or not 1). So, the Hypothesized slope coefficient will be 1.
From the t-statistic, we can rearrange the formula to find the Standard Error:
Standard Error = (Estimated slope coefficient - Hypothesized slope coefficient) / t
Plugging in the values, we have:
Standard Error = (0.9 - 1) / -3.6
Simplifying, we get:
Standard Error ≈ -0.1 / -3.6
Standard Error ≈ 0.0278
Therefore, the estimated standard error for the estimated slope coefficient is approximately 0.0278.