Respond to all the questions appropriately.

1.Measuring GDP (6pts): A simple economy has four industries:

? The agricultural industry sells $45 million in food products directly to households as well as $35

million to the steel industry, which turns the food into biofuel for their factories.

? The iron mining industry produces iron, all of which is sold to the steel industry. Total sales to the

steel industry are $200 million per year.

? The coke industry produces coke which is combined with iron to make steel. Total sales to the steel

industry are $45 million per year.

? The steel industry processes the iron and coke together to make steel. The steel industry sells $300

million to the auto industry to make cars per year. Assume another $50 million is sold directly to

consumers/households and companies to put up steel fencing around their properties.

? The auto industry uses steel from the steel industry as well as other inputs (that it creates on its own)

to sell $725 million in vehicles to the public.

What is the GDP?

\fA university wishes to analyse the performance of its students on a particular degree course. It records the scores obtained by a sample of 12 students at entry to the course, and the scores obtained in their final examinations by the same students. The results are as follows: Student A B C D E H K L Entrance exam score x (%) 86 53 71 62 70 55 58 72 Finals paper score y (%) 75 60 74 68 70 75 78 90 85 62 70 x = 836 _y =867 _x2 = 60.016 _y' =63,603 )(x-x)(y- y) =1,122 (i) Calculate the fitted linear regression equation of y on x. (ii) Assuming the full normal model, calculate an estimate of the error variance oz and obtain a 90% confidence interval for o?. (iii) By considering the slope parameter, formally test whether the data is positively correlated. (iv) Calculate a 95% confidence interval for the mean finals paper score corresponding to an individual entrance score of 53. (v) Test whether this data could come from a population with correlation coefficient equal to 0.75. (vi) Calculate the proportion of variation explained by the model. Hence, comment on the fit of the model