Partition matrices: Consider using a partition matrix in OLS. That is, consider X = [X1,X2] and = 1 2 where X1 is n × r1, X1 is n × r2, 1 is r1 × 1, 2 is r2 × 1, and r1 + r2 = r, the overall number of columns in X. When we take the inverse of a 2 × 2 partition matrix A B C D −1 = (A − BC−1D)−1 −(A − BD−1C)−1BD−1 −(D − CA−1B)−1CA−1 (D − CA−1B)−1 Find the equations for ˆ 1 and ˆ 2 using the OLS estimator ˆ = (X0X)−1X0y

7

step-by-step explanation:

i'm assuming you need to figure out how many campers go into each tent.

i got the answer by:

24+4=28

28/4=7  

3

step-by-step explanation:

divide 13.5 by 9 to get the scale factor. it equals 1.5

2 * 1.5 = 3

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.