Question

Using the Ordinary Least Squares (OLS) method, a researcher estimated the relationship between initial salary ($S$) of MBA graduates and their cumulative grade point average (CGPA) as $\hat S_i=\hat\beta_0+\hat\beta_1\,CGPA_i,\ i=1,2,\ldots,100$, where $\hat\beta_0=4543$ and $\hat\beta_1=645.08$. The standard errors of $\hat\beta_0$ and $\hat\beta_1$ are $921.79$ and $70.01$, respectively. The $t$-statistic for testing the null hypothesis $\beta_1=0$ is _____{(round off to two decimal places)

Hint:

For a single coefficient test in OLS: $t=\dfrac{\hat\beta_j-\beta_{j,0}}{SE(\hat\beta_j)}$. Only the coefficient’s own standard error enters the denominator.

Answer 1

Correct Answer: 9.2

Step 1: Test statistic. For $H_0:\beta_1=0$, the $t$ statistic is \[ t=\frac{\hat\beta_1-0}{SE(\hat\beta_1)}=\frac{645.08}{70.01}. \] Step 2: Compute and round.
$\displaystyle \frac{645.08}{70.01}=9.2141\ldots \Rightarrow$ rounded to two decimals $= \boxed{9.21}$.