Linear
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Tutorial
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Linear Regression Tutorial: Analyzing Frog Croaking vs Temperature, Slides of Computational Methods
A matlab tutorial on performing linear regression analysis to determine the relationship between frog croaking frequency (cph) and temperature (t °f). The tutorial includes the matlab code for generating a scatter plot, calculating regression coefficients, and assessing the goodness of fit.
Typology: Slides
2012/2013
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Linear
Regression
Tutorial
A plotting Grid
- Lets Make some SCATTER
The MATLAB code
% B. Mayer 20Feb07 * ENGR % 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 m disp('Slope Parameter, m0') m0 = (sumXsumY - nsumXY)/(sumX^2 - nsumXX) % % Calc optimum intercept term b disp('Intercept Parameter, b0') b0 = (sumY - m0*sumX)/n %
The MATLAB code
% Plot Regression Line Tfmax = max(Tf); Tfmin = min(Tf); Tfplot = linspace(Tfmax, Tfmin); % Calc CpH projected response using Regression Constanstants CpHplot = m0Tfplot + 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, J 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)
The MATLAB Results
Diplaying Scatter Plot - Hit any key to
continue
sumX =
1.1996e+
sumY =
249.
n =
15
sumXY =
2.0090e+
sumXX =
9.6568e+
Slope Parameter, m
m0 =
0.
Intercept Parameter, b
b0 =
-0.
Diplaying °F Regression Plot - Hit any key to
continue
J0 =
12.
CpH_avg =
16.
S =
41.
Coeff of Determination, r-sqd =
0.
By Excel
- Use to Check m0, b0, and r
2
Frog Croaking
CpH = 0.2157•Tf - 0. R^2 = 0.
15
16
17
18
19
20
70 75 80 85 90 95 Temperature (°F)
Croak Frequency (Croaks per Hour)
E25_Lin_Regress_Tutorial_0703.xls