What Is the Y-Hat Formula?

By Staff WriterLast Updated Mar 27, 2020 10:30:18 PM ET

According to Michigan State University, Y-hat is equal to the intercept plus the slope times X. X represents any number for which the researcher wants to know the predicted dependent variable.


Y-hat is the prediction of the effect of an independent variable on the dependent variable, states the Department of Mathematics and Computer Science at Hobart and William Smith Colleges. Within the regression line, Y-hat is the inference that regression analysis makes concerning the data. These values show a correlation, not causation, between the data points.

The distance between the regression line and data points are the residuals of the regression model. The regression line contains a “best fit” line that is the linear production of the sum of the squares of the data points. The predicted values not on the best fit line are the residuals in the equation. The residuals account for all the raw data that is not a part of the regression model. The more residuals present, the greater the standard error of the estimate in the equation.

According to Dr. Russell Campbell at University of Northern Iowa, the points for Y-hat are perpendicular to the linear regression line. Dr. Campbell notes that using the regression line formula to find Y-hat is an estimation technique.