The annual maintenance bills of similar buildings in down town Nairobi were related to their age with the following results.
First row age A. Age (yrs) and second row M. Maintenance bills (000 shs)

Age 15 5 25 40 5 20 10 30 445 15 25 35 10 30
M 39 24 115 105 50 86 67 90 140 112 70 186 43 126

a) fit a regression line to this data (5 marks)

b) find the 95 % confidence interval estimate of the maintenance cost of the building for
age in years, assuming the data is homoscedastic (5 marks)

c) Test the significance of the regression coefficients b and a at the .05 significance level (5 marks)

y=3x+4

step-by-step explanation:

given the points a(0,4) and b(-4, -8)

eqn of line ab: (y-4)/(x-0)=(-8-4)/(-4-0)

(y-4)/x=-12/-4=3

y=3x+4

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.

the ordered pairs for the given function are of the form