solution:
(a) Using the calculator (LinReg(a+bx) L1, L2, Y1) , we find = 64.94 + 0.634(age ), r =
0.993. The large value of r tells us that the points are close to a line. The scatterplot and LSLR
are shown below on the graph at the left.From the graph on the left, a line appears to be a good fit for the data (the points lie close to the
line). The residual plot on the right shows no readily obvious pattern, so we have good evidence
that a line is a good model for the data and we can feel good about using the LSRL to predict
height from age.
(b) The residual (actual minus predicted) for age = 19 months is 77.1 – (64.94 + 0.634 · 19) = 0.114.
Note that 77.1–Y1(19) = 0.112 .(Note that you can generate a complete set of residuals, which will match what is stored in RESID
, in a list. Assuming your data are in L1 and L2 and that you have found the LSRL and stored it in
Y1 , let L3 = L2–Y1(L1) . The residuals for each value will then appear in L3 . You might want
to let L4 = RESID (by pasting RESID from the LIST menu) and observe that L3 and L4 are the
same.Digression: Whenever we have graphed a residual plot in this section, the vertical axis has been the
residuals and the horizontal axis has been the x -variable. On some computer printouts, you may see the
horizontal axis labeled “Fits” (as in the graph below) or “Predicted Value.”