One general belief held by observers of the business world is that taller men earn more money than shorter men. In a study reported in the Wall Street Journal, 30 MBA graduates, all about 30 years old, were surveyed and asked to report their annual incomes and their heights. These responses are recorded in MBA.xlsx.

a     Estimate a linear relationship between heights and annual income of MBA graduates and interpret your results.

b     Do these data provide sufficient statistical evidence to infer at the 5% significance level that taller men with MBAs earn more money than shorter ones?

c     Provide a measure of the strength of the linear relationship between income and height.

d     Obtain three measures to check the fitness of the model. Do you think that this model is good enough to be used to estimate and predict income on the basis of height? If not, explain why not. If so,

i         predict the income of 183cm tall men with MBAs.

ii        estimate with 95% confidence the mean income of all 183 cm tall men with MBAs

iii      predict with 95% confidence the income of a 183 cm tall man with an MBA.

Height	Income ($)
175.0	68660
167.5	74820
172.5	69260
175.0	79620
162.5	69180
182.5	66700
160.0	71140
175.0	83680
172.5	70060
182.5	77480
170.0	61340
165.0	61180
177.5	74740
170.0	78940
182.5	80540
182.5	75080
175.0	80980
177.5	75940
172.5	69640
182.5	74640
187.5	68120
170.0	65980
172.5	74060
190.0	72280
177.5	75840
165.0	67020
172.5	73520
162.5	67680
167.5	70720
175.0	80340