show work please!

Question 5 (a) Twelve families of City A are randomly selected, their annual disposable income (1:, in $000) and total annual consumption (y, in $'000) are summarized below: Ex = 3370, 2 y = 3502.65, 2x2 =1628900,Ey2 = 13020211241, ny =1444507 (i) Find the 'best t' line of total annual consumption on annual disposable income. [4 marks] (ii) Interpret the regression coefficient estimates. [2 marks] (iii) Estimate the total annual consumption of a family with an annual disposable income of $380,000. [2 marks] (b) In estimating a multiple linear regression equation of operating cost 0;, in $000) on production (1:1, in tons), machine hours (1:2, in hours), variable overhead cost (x3, in $000) and direct labour hours (3:4, in hours) of a company, data of 27 months are used and some computer outputs are provided below. Coefcients 5 l .723 1 0.9479 2.4710 0.0483 -0.0506 Regression 2271423 b d 1' Residual 11 c e Total 2274122 26 (i) Write down the 'best t' equation. [2 marks] (ii) What is the proportion of variation in operating cost that can be explained by the tted equation in (i)? [2 marks] (iii) Test the signicance of the overall model at 1% level of signicance. [4 marks] (iv) Test whether machine hours has signicant effect on operating cost at 5% level of signicance. [4 Mk3]