Suppose that X ~ U (0, a) where a is a constant. Let Y = X². Calculate the %3D correlation coefficient p(X,Y).

A correlation of zero between two quantitative variables means that

The following table shows the number of fiber optic cable connections to homes in a country from 2000 to 2004 (t = 0 represents 2000). Year t 0 1 2 3 4 Connections c (Thousands) 5 15 30 70 155 (a) Use technology to obtain the linear regression line and the correlation coefficient r, with all coefficients rounded to two decimal places. c(t) =       r  =

Early in the twentieth century, an intelligence test called the Stanford-Binet Test (more commonly known as the IQ test) was developed. In this test, an individual’s mental age M is divided by the individual’s chronological age C and then the quotient is multiplied by 100. The result is the individual’s IQ. IQ(M, C) = M C × 100                                                                                      Find the partial derivatives of IQ with respect to M and with respect to C. Evaluate the partial derivatives at the point (12, 10) and interpret the result.