performing linear regression fits using cftool based on data points

I want to use the MATLAB curve fitting tools (cftool) to prediction intervals (compute 95% prediction intervals about th linear regression). I want to implement the following example problem for prediction intervals at x = 500 based on 13 data points and a linear regression fit.

(from J. Devore, Probability and Statistics for Engineering and the Sciences, 7th Ed., Brooks/Cole, Belmont, CA 2009, page 446)

x = [398 292 352 575 568 450 550 408 484 350 503 600 600]

y = [0.15  0.05  0.23  0.43  0.23  0.4 0.44  0.44  0.45  0.09  0.59  0.63  0.6]

Something like?

Answer 1

[Sam Chak]

@Jamie Al

Does it look like this?

x = [398 292 352 575 568 450 550 408 484 350 503 600 600];
y = [0.15  0.05  0.23  0.43  0.23  0.4 0.44  0.44  0.45  0.09  0.59  0.63  0.6];
[~, idx] = sort(x);
ysort = y(idx);
xsort = x(idx);
mdl = fitlm(xsort, ysort)

plot(xsort, ysort, 'o')
grid on
xlabel('x')
ylabel('y')
hold on
xfit = linspace(min(xsort), max(xsort), 13);
yfit = 0.001432*xfit - 0.3115;
plot(xfit, yfit, 'r', 'linewidth', 1.5)
hold off

[Jamie Al]

Looks good to me, I was wondering if I can recreate this red and blue dashed lines in MATLAB

[Sam Chak]

If you know the formulas for the 95% Confidence Interval and 95% Prediction Interval, then it is possible to plot the blue and red dashed curves. Follow my code (before the hold off line) and insert the formulas given here:

https://www.real-statistics.com/regression/confidence-and-prediction-intervals/

yCI = ...;
yPI = ...;
plot(xfit, yCI, '--b', 'linewidth', 1.5)
plot(xfit, yPI, '--r', 'linewidth', 1.5)
hold off