Computer regression output

One row per coefficient, one column per fact about it. Here is a block for 20 apartments, with $x$ the distance from campus in miles and $y$ the monthly rent in dollars.

$S = 77.73$, R-Sq $= 81.0\%$, R-Sq(adj) $= 79.9\%$

The equation comes out of the Coef column and nowhere else. The Constant row holds the y-intercept and the row named after the explanatory variable holds the slope, so $\hat{y} = 1492.51 - 105.52x$ (read y-hat). At two miles out that predicts $1492.51 - 105.52(2) = 1281.47$ dollars. $S$ is the standard deviation of the residuals: typical miss, about 78 dollars. R-Sq is $r^2$, and since $\sqrt{0.810} = 0.900$ and the slope is negative, $r = -0.900$.

Two cells get misread constantly. "$S = 77.73$ is the standard error of the slope" is wrong: that number is the SE Coef entry on the slope's own row, 12.05 dollars per mile, while $S$ carries the units of the response. And "R-Sq is 81.0%, so $r = 0.81$" is wrong twice, because $r$ is the square root rather than the value itself, and because $r^2$ has thrown the sign away. You get the sign back from the slope, never from the table alone.

SE Coef, T and P describe how precisely each coefficient was estimated: T is simply Coef divided by SE Coef, and $-105.52 / 12.05 = -8.76$ checks out. Those three columns belong to inference for regression slopes, which the Fall 2026 AP Statistics course does not contain. Read past them. A P of 0.000 is a rounded display, not a probability of zero, and R-Sq(adj) only earns its keep once a model has more than one predictor.