<p>Normally an exam question like that can be solved by simply calculating the <span class="math-container">$t$</span>-statistics which can be simply done as:</p>
<p><span class="math-container">$$t_{\hat{\beta}} = \frac{\hat{\beta}-\beta_0}{se(\hat{\beta})}$$</span></p>
<p>where <span class="math-container">$\hat{\beta}$</span> is the estimate, <span class="math-container">$\beta_0$</span> is the assumed value of beta under null (usually 0) and <span class="math-container">$se(\hat{\beta})$</span> standard error of the coefficient and then compare it to <span class="math-container">$5\%$</span> critical value (for large <span class="math-container">$n$</span> and two sided hypothesis approximately <span class="math-container">$1.96$</span>).</p>
<p>However, you should ask your teacher/supervisor to clarify what is considered 'sophisticated calculation' - some might consider even subtraction and division sophisticated. An approximate rule of thumb that requires even less calculation is to see if the coefficient <span class="math-container">$\hat{\beta}$</span> (and assuming null hypothesis assumes <span class="math-container">$\beta_0=0$</span>) is twice as large as the standard error.</p>

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2020-08-03T14:09:06.403Z
2020-08-03T14:09:06.403Z
1muflon1
<p>I have a question that contains a list of parameter estimates and their related standard errors. It then goes on to ask that I explain how I know all parameter estimates are statistically significant at a 5% significance level, but without performing any 'sophisticated calculations'. Does this mean I have to compare the standard errors to the estimators or do I find their t-values?</p>

<econometrics><regression>
How can you find all parameter estimates are statistically significant but without performing any sophisticated calculations?
Esther Blaese
# How can you find all parameter estimates are statistically significant but without performing any sophisticated calculations?

(Asked by: username_0 on 2020-08-03)

I have a question that contains a list of parameter estimates and their related standard errors. It then goes on to ask that I explain how I know all parameter estimates are statistically significant at a 5% significance level, but without performing any 'sophisticated calculations'. Does this mean I have to compare the standard errors to the estimators or do I find their t-values?

**Tags:** econometrics, regression

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## 1 answers

### Answer by username_1 on 2020-08-03. Score: 3

Normally an exam question like that can be solved by simply calculating the $t$-statistics which can be simply done as:

$$t\_{\hat{\beta}} = \frac{\hat{\beta}-\beta\_0}{se(\hat{\beta})}$$

where $\hat{\beta}$ is the estimate, $\beta\_0$ is the assumed value of beta under null (usually 0) and $se(\hat{\beta})$ standard error of the coefficient and then compare it to $5\%$ critical value (for large $n$ and two sided hypothesis approximately $1.96$).

However, you should ask your teacher/supervisor to clarify what is considered 'sophisticated calculation' - some might consider even subtraction and division sophisticated. An approximate rule of thumb that requires even less calculation is to see if the coefficient $\hat{\beta}$ (and assuming null hypothesis assumes $\beta\_0=0$) is twice as large as the standard error.


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