The least squares estimate for the coefficient of a multivariate regression model is exactly regression through the origin with the linear relationships.

The correct answer is False.

The least squares estimate for the coefficient of a multivariate regression model is not exactly regression through the origin with the linear relationships. The least squares estimate is a linear combination of the data points, and it will not always pass through the origin.

In addition, the least squares estimate is not always the best estimate of the coefficient. There are other methods of estimation that can be used, such as maximum likelihood estimation.

The least squares estimate is a common method of estimation, but it is not always the best method. It is important to understand the limitations of the least squares estimate before using it.