Question Two Consider the following statements: a) A matrix Amxn is nonsingular ar b) Amxn is square c) Amxn has linear independence d) The rank of Am×n is r(A) = min{m, n} Use "necessary condition”, “sufficient condition”, or “necessary and sufficient condition” to describe how Statement a) is related to Statements b), c), and d). Here are the conditions • Necessary Condition: q constitutes a necessary condition of p; mathematically, pq, read as: if p, then q; or, p implies q • Sufficient Condition: q is a sufficient condition for p; mathematically, p = q, read as: p if q; or, if q, then p; or, q implies p • Necessary and Sufficient Condition: q is both necessary and sufficient for p; mathematically, pq, read as: p if and only if q

Plot the logarithm of arrivals for each transportation mode against time, all on the same graph. Which now appears to be growing the fastest?

Estimate the double-log (log linear) time trend model for log cruise ship arrivals against log time. Estimate a linear time trend model of cruise ship arrivals against time. Calculate the root mean square error between the predicted and actual value of cruise ship arrivals. Is the root mean square error greater for the double log non-linear time trend model or for the linear time trend model?