Question

How do you calculate the t-score of the slope of a time series regression?

Answer 1

Hint: We need to calculate the t-score of the slope of a time series regression. The t-score formula is used for solving probability questions. The formula is the ratio of difference of the actual regression coefficient and hypothesized population Regression coefficient to the Standard error of Regression coefficient.

Complete step by step solution:
We need to calculate the t-score of the slope of a time series regression.
The t-score formula helps us to take the individual scores and convert them into a standardized form. It helps us to compare the scores.
It is usually denoted by $t$
The value of the t-score is influenced by certain factors that are given as follows,
1. The mean of the population from which the given sample is drawn
2. The mean of the given sample.
3. The mean of the population from which the given sample is drawn
4. The standard deviation of the sample.
The formula of t-score of the slope of a time series regression is given by
$\Rightarrow t=\dfrac{b-B}{{{s}_{b}}}$
Here,
t is the t-score;
b is the actual regression coefficient
B is the hypothesized population Regression coefficient
${{s}_{b}}$ is the standard error of the Regression coefficient.
The regression coefficient is the value that tells us about the change in the value of a dependent variable with the change in the independent variable.
The standard error is the measure of the standard deviation of the coefficient of regression usually denoted by ${{s}_{b}}$

Note: We use the t-score formula when we do not know the population standard deviation and you are given a small sample. Higher values of the t-score indicate a large difference between the given samples. Smaller differences indicate similarities between the given samples.