Question: In a random sample of n pairs of values of
In a random sample of n pairs of values of X and Y, (xi, yj) occurs fij times for i = 1, 2, . . . , r and j = 1, 2, . . . , c. Letting fi, denote the number of pairs where X takes on the value xi and fj the number of pairs where Y takes on the value yj, write a formula for the coefficient of correlation.
Answer to relevant QuestionsIf b is the column vector of the β’s, verify in matrix notation that q = (Y – Xb)'(Y – Xb) is a minimum when b = B = (X'X)–1(X'Y). With x01, x02, . . . , x0k and X0 as defined in Exercise 14.39 and Y0 being a random variable that has a normal distribution with the mean β0 + β1x01 + · · · + βkx0k and the variance σ2, it can be shown that Is a ...Use the coding of Exercise 14.15 to rework both parts of Exercise 14.45. In exercise When the x’s are equally spaced, the calculation of and can be simplified by coding the x’s by assigning them the values . . . ,- ...With reference to Exercise 14.43, construct a 99% confidence interval for the regression coefficient β. In exercise The following are the scores that 12 students obtained on the midterm and final examinations in a course ...Redo Exercise 14.61 when the dosage is 20 milligrams. Note the greatly increased width of the confidence limits for the expected number of deaths and of the limits of prediction. This example illustrates that extrapolation, ...
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