## Forcing regression through a given point using any familiar computational routineThis report describes a simple method for obtaining the prediction equation best fit to all data points (in the least squares sense) while forcing an exact fit at any known point. The decision to constrain the solution at a point should be justified on theoretical grounds without appeal to data. Examples are given. When required any familiar regression program can be forced to select the best line through a given point by simply adjusting and extending the data entry. All necessary changes to the program results (test statistics and estimates of regression parameters) can be accomplished without modifying the computer program. (Author). |

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### Contents

CONVERSION FACTORS U S CUSTOMARY TO METRIC SI | 5 |

A PROBLEM WITH THE CUSTOMARY APPROACH | 11 |

Real test data for example problem 1 | 17 |

### Common terms and phrases

28 cm.—(Technical paper Army Coastal Engineering available from NTIS beach slope Celsius Coastal Engineering Research constrained Corps of Engineers Correlation coefficient Cover title customary computational routines Data analysis data points describes a simple Edward Engineering Research Center equa equation best fit Estimated residual variance exact fit example problem Examples are given extended data set F-value Fahrenheit FAMILIAR COMPUTATIONAL ROUTINE forcing an exact ft/s given point Hands.—Fort Belvoir independent variables kilograms known point least squares sense linear method for obtaining modifying customary computational multiple regression necessary changes number of independent observed data set Obsn obtaining the prediction paper Coastal Engineering predicted values prediction equation best principle of least program results putational routine regression program Report describes Research Center U.S. results are accomplished simple method simple regression Springfield squared deviation Standard error sum of squares surf zone Technical paper Coastal test statistics wave energy flux wave forces Y-intercept zero zero-intercept