y = X,B1 + X,B2 + ɛ where y = (y1, .., Yn)', X1 and X2 are random except the intercept term (i.e., th vector of 1) included in X1. Conditional on Xı and X2, the random error vecte ɛ is jointly normal with zero expectation and variance-covariance matrix V, which does not depend on X1 and X2. V is not a diagonal matrix (i.e., some off-diagonal elements are nonzero). B1 and B2 are vectors of two different sets of regression coefficients; B1 has two regression coefficients and B2 has four regression coefficients. B = (B1 , B½)'; that is, B is a column vector of %3D six regression coefficients. a) V is completely known (i.e., the values of all elements of V are given).

The least-squares regression line relating two statistical variables is given as  = 24 + 5x. Compute the residual if the actual (observed) value for y is 38 when x is 2.     4           38     2

Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed.  The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.72, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4.  The regression intercept is reported as 28.  The sum of squares in regression (SSR) is reported as 72000 and the sum of squared errors (SSE) is 28000.  From this information, what is MSE/MST? (a) .4000 (b) .3000 (c) .5000 (d) .2000 (e) NONE OF THE OTHERS

Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 21 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed.  The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.9, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4.  The regression intercept is reported as 28.  The sum of squares in regression (SSR) is reported as 90000 and the sum of squared errors (SSE) is 10000.  From this information, what is the number of degrees of freedom for the t-distribution used to compute critical values for hypothesis tests and confidence intervals for the individual model…