Question

A local trucking company fitted a regression to relate the travel time (days) of its shipments as a function of the distance traveled (miles). The fitted regression is Time = −7.126 + 0.0214 Distance, based on a sample of 20 shipments. The estimated standard error of the slope is 0.0053. Find the value of tcalc to test for zero slope.

Answer 1

Answer:

4.038

Step-by-step explanation:

The simple regression model is:

$Time = \hat\beta _{0} + \hat\beta_{1}Distance = -7.126 + 0.0214Distance$, then $\hat\beta_{1} = 0.0214$.

The statistic calculated for the hypothesis test of statistical significance, for the slope, in a simple regression model is given by:

$t_{c} = \frac{\hat\beta_{1}-\beta_{1_{0}}}{SE}$

with $\hat\beta_{1}$  the slope estimator, $\beta_{1_{0}}$  the value of slope in the null hypothesis and $SE$ the standard error of the slope. Thus,

$t_{c} = \frac{0.0214-0}{0.0053} = 4.038$