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

4.038

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) = (0.0214-0)/(0.0053) = 4.038`