ON A PROBLEM OF FIXING THE LEVEL OF INDEPENDENT VARIABLES IN A LINEAR REGRESSION FUNCTION.
NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES
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Suppose that a linear regression model Y betax U is given. It is desirable to fix x so as to make EY betax as near to some prescribed level c as possible. Asymptotic consideration leads to a solution of the type x circumflex cMbeta circumflexbeta circumflexMbeta circumflex ksigma circumflexsquared where beta circumflex is the least square estimator of beta, and sigma circumflexsquared is the unbiased estimator of sigma squared VU. Under the assumption of normality for the distribution of U, an exact formula for the first two moments of the error betax circumflex is given, and by expanding the formula for the mean square error it is recommended that k be chosen to be equal to max 5-p,0 where p is the dimension of the x vector. Author
- Statistics and Probability