Linear Regression of Motor Power Consumption on Speed and Load Using fitlm

Project info

• Field of studyRobotics and Mechatronics
• LevelUndergraduate thesis (S1)
• Method typeStatistics and Regression
• Estimated build time± 3 working days
• Toolsfitlm, anova, coefCI, plotResiduals (Statistics and Machine Learning Toolbox)
• PriceUS$19 - US$122

Research goal

Model the motor power consumption as a function of the motor speed and the motor load using fitlm regression and assess the model fit.

Variables

Example result

• 0.789R-squared
• 0.788Adjusted R-squared
• 1.014RMSE
• 1.669Coef. Motor speed
• -2.092Coef. Motor speed
• 347Observations

Linear regression of Motor power consumption on Motor speed and Motor load yields an R-squared of 0.789 (adjusted 0.788) and RMSE 1.014; the coefficients are Motor speed=1.669 and Motor load=-2.092 with 95% confidence intervals excluding zero.

Computed from illustrative synthetic data, not from a real study.

About Linear Regression with fitlm

fitlm builds a linear regression model from a data table and provides coefficients, significance tests, R2, and residual diagnostics. It suits theses that test the effect of several predictors on one response.

Steps

1. 1Arrange the data in a table with clear variable names
2. 2Write the model formula, for example y ~ x1 + x2
3. 3Fit the model with fitlm
4. 4Read coefficients, p-values, R2, and adjusted R2
5. 5Check residual assumptions (normality, constant variance)
6. 6Compute coefficient confidence intervals and plot diagnostics

Assumptions to check

• Linear relationship between predictors and response
• Residuals are normal with constant variance and independent
• Predictors are not highly collinear

Reading and reporting the results

Report coefficients with standard errors, p-values, confidence intervals, adjusted R2, and the model F test. Discuss assumption violations and influential observations (Cook's distance) if any.

Example MATLAB code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

rng(1);
n = 150;
motor_speed = 50 + 10*randn(n, 1);
motor_load = 20 + 5*randn(n, 1);
motor_power_consumption = 5 + 0.8*motor_speed - 1.2*motor_load + 4*randn(n, 1);

tbl = table(motor_speed, motor_load, motor_power_consumption, 'VariableNames', {'motor_speed', 'motor_load', 'motor_power_consumption'});
mdl = fitlm(tbl, 'motor_power_consumption ~ motor_speed + motor_load');
disp(mdl);
fprintf('R2 = %.3f, adjusted R2 = %.3f, RMSE = %.3f\n', ...
    mdl.Rsquared.Ordinary, mdl.Rsquared.Adjusted, mdl.RMSE);
disp(coefCI(mdl));
disp(anova(mdl, 'summary'));

[~, pSW] = lillietest(mdl.Residuals.Raw);
fprintf('Residual normality (Lilliefors) p = %.3f\n', pSW);

figure;
subplot(1,3,1); plotResiduals(mdl, 'probability');
subplot(1,3,2); plotResiduals(mdl, 'fitted');
subplot(1,3,3); plot(mdl.Fitted, tbl.motor_power_consumption, '.'); hold on; refline(1, 0);
xlabel('Fitted'); ylabel('Actual');

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions