1. MTH16_Lec-07a_sec_7-4.pptx 1 Bruce Mayer, PE Mathematics-16: Applied Calculus II Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Mathematics 16 Linear Regression Tutorial

2. MTH16_Lec-07a_sec_7-4.pptx 2 Bruce Mayer, PE Mathematics-16: Applied Calculus II A plotting Grid  Lets Make some SCATTER

3. MTH16_Lec-07a_sec_7-4.pptx 3 Bruce Mayer, PE Mathematics-16: Applied Calculus II

4. MTH16_Lec-07a_sec_7-4.pptx 4 Bruce Mayer, PE Mathematics-16: Applied Calculus II

5. MTH16_Lec-07a_sec_7-4.pptx 5 Bruce Mayer, PE Mathematics-16: Applied Calculus II

6. MTH16_Lec-07a_sec_7-4.pptx 6 Bruce Mayer, PE Mathematics-16: Applied Calculus II xy 02 56 1011 Example

7. MTH16_Lec-07a_sec_7-4.pptx 7 Bruce Mayer, PE Mathematics-16: Applied Calculus II Do On WhiteBoard xy 02 56 1011 Example

8. MTH16_Lec-07a_sec_7-4.pptx 8 Bruce Mayer, PE Mathematics-16: Applied Calculus II

9. MTH16_Lec-07a_sec_7-4.pptx 9 Bruce Mayer, PE Mathematics-16: Applied Calculus II

10. MTH16_Lec-07a_sec_7-4.pptx 10 Bruce Mayer, PE Mathematics-16: Applied Calculus II [eqn (7)]

11. MTH16_Lec-07a_sec_7-4.pptx 11 Bruce Mayer, PE Mathematics-16: Applied Calculus II Regression Example  Do Frogs Croak More on WARM Nites?  Go to Frog Pond Take Temperature Count Croaks Temperature (ºF)Croaks/Hr 88.620.0 71.616.0 93.319.8 84.318.4 80.617.1 75.215.5 69.714.7 82.017.1 69.415.4 83.316.2 78.615.0 82.617.2 80.616.0 83.517.0 76.314.1

12. MTH16_Lec-07a_sec_7-4.pptx 12 Bruce Mayer, PE Mathematics-16: Applied Calculus II The MATLAB code % B. Mayer 20Feb07 * MTH16 % Linear Regression Tutorial % E25_Lin_Regress_Tutorial_0703.m % clear % % Define Data Vectors for Croaking Frogs Tf = [69.4, 69.7, 71.6, 75.2, 76.3, 78.6, 80.6, 80.6, 82, 82.6, 83.3, 83.5, 84.3, 88.6, 93.3]; % T in °F CpH = [15.4, 14.7, 16, 15.5, 14.1, 15, 17.1, 16, 17.1, 17.2, 16.2, 17, 18.4, 20, 19.8]; % CPH is "Croaks per Hour" % % Plot CpH(T) plot(Tf, CpH,'*'), xlabel('T °F'), ylabel('CpH (Croaks/Hr)'),... Title('Frog Croaking vs Temperature'), grid % disp('Diplaying Scatter Plot - Hit any key to continue ') pause % % Calc Linear Regression Coefficient terms using Absolute Temps sumX = sum(Tf) sumY = sum(CpH) n = length(Tf) sumXY = sum(Tf.*CpH) sumXX = sum(Tf.*Tf) % % Calc optimum slope term m0 disp('Slope Parameter, m0') m0 = (sumX*sumY - n*sumXY)/(sumX^2 - n*sumXX) % % Calc optimum intercept term b0 disp('Intercept Parameter, b0') b0 = (sumY - m0*sumX)/n %

13. MTH16_Lec-07a_sec_7-4.pptx 13 Bruce Mayer, PE Mathematics-16: Applied Calculus II The MATLAB code % Plot Regression Line Tfmax = max(Tf); Tfmin = min(Tf); Tfplot = linspace(Tfmax, Tfmin); % Calc CpH projected response using Regression Constanstants CpHplot = m0*Tfplot + b0; plot(Tf, CpH,'*', Tfplot, CpHplot), xlabel('T °F'), ylabel('CpH (Croaks/Hr)'),... Title('Frog Croaking vs Temperature'), grid % disp('Diplaying °F Regression Plot - Hit any key to continue ') pause % % Calc Goodness of Fit % the Minimized J value, J0 J0 = sum((m0*Tf+b0-CpH).^2) % Calc Sum of Sqs about the Mean CpH_avg = mean(CpH) S = sum((CpH-CpH_avg).^2) % Calc r-sqd r_sqd = 1-J0/S; % disp('Coeff of Determination, r-sqd = ') disp(r_sqd)

14. MTH16_Lec-07a_sec_7-4.pptx 14 Bruce Mayer, PE Mathematics-16: Applied Calculus II The Regression Plot

15. MTH16_Lec-07a_sec_7-4.pptx 15 Bruce Mayer, PE Mathematics-16: Applied Calculus II The MATLAB Results Diplaying Scatter Plot - Hit any key to continue sumX = 1.1996e+003 sumY = 249.5000 n = 15 sumXY = 2.0090e+004 sumXX = 9.6568e+004 Slope Parameter, m0 m0 = 0.2157 Intercept Parameter, b0 b0 = -0.6152 Diplaying °F Regression Plot - Hit any key to continue J0 = 12.6107 CpH_avg = 16.6333 S = 41.9933 Coeff of Determination, r-sqd = 0.6997

16. MTH16_Lec-07a_sec_7-4.pptx 16 Bruce Mayer, PE Mathematics-16: Applied Calculus II By Excel  Use to Check m0, b0, and r 2 