This study addresses predicting the relationship between forward speed and propeller speed of an autonomous underwater vehicle (AUV) with a towed flexible cable using multiple regression analysis. Accurate prediction of the propeller speed corresponding to forward speed is important. The prediction requires considering various factors such as the dynamic behavior of a flexible cable, tidal currents, and AUV motions. The regression analysis based on in-service data of the AUV, therefore, established the relation between the forward speed and propeller speed considering the other factors. On the other hand, minimal independent variables in the regression model are desirable to avoid multicollinearity and overfitting. Variable selection based on the t-Test and sparse modeling was carried out to remove insignificant variables. We confirmed that the regression model presented in this study was in agreement with the observed data sufficiently, and the residuals of the regression model followed a normal distribution. The propeller speed predicted by the regression model considering only the forward speed of the AUV was comparable to the result predicted by the CFD calculation, not including the other factors. The result indicates the regression analysis can validate the results based on experiments and a numerical simulation.