The regression plane in three dimensions

remains constant. Similarly, b2 gives the response of Y to a unit change in X2, given no change in Xv If X1 and X2 both change by 1, then the effect on Y is b1 + b2. b1 and b2 are both estimates of the true parameters P1 and and so standard errors and confidence intervals can be calculated, implying that we are not absolutely certain about the true position of the plane. In general, the smaller these standard errors, the better, since it implies less uncertainty about the true relationship between Y and the X variables.

When there are more than two explanatory variables, more than three dimensions are needed to draw a picture of the data. The reader will understand that this is a difficult (if not impossible) task; however, it is possible to estimate such a model and interpret the results in a similar manner to the more simple model.

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