35.3 Regression using software
In the population, the intercept is denoted by β0 and the slope is denoted by β1. These population values are unknown, and are estimated by the statistics b0 and b1 respectively.
The formulas for computing b0 and b1 are ugly, so we will use software to do the calculations. As usual, the values of these population parameters are unknown, and the values of the sample statistics will change from sample to sample (so they have sampling variation).
For the red deer data again
(Fig 33.2),
part of the relevant output is
shown in
Fig. 35.3 (using jamovi) and
Fig. 35.4 (using SPSS).
From the output,
the slope b1 in the sample is b1=−0.181,
and the y-intercept b0 in the sample is b0=4.398.
That is,
the values of b0 and b1 are in the column labelled Estimate
in jamovi,
or the column labelled B
in SPSS.
These are the values of the two regression coefficients;
then
ˆy=4.398+(−0.181×x), which is usually written more simply as
ˆy=4.398−0.181x.

FIGURE 35.3: jamovi output for the red-deer data

FIGURE 35.4: SPSS output for the red-deer data

FIGURE 35.5: jamovi output for the cyclone data