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(a) Twelve families of City A are randomly selected, their annual disposable income (x, in $'000) and total annual consumption (y, in $'000) are summarized below: Ex =3870, _ v =3502.65, _x2 =1628900, > > =1302023.1241, Exy =1444507 (1) Find the "best fit' 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 (y, in $'000) on production (1, in tons), machine hours (x,, in hours), variable overhead cost (X, , in $'000) and direct labour hours (x4, in hours) of a company, data of 27 months are used and some computer outputs are provided below. Variable Coefficients Standard error Intercept 51.7231 21.7040 0.9479 0.1200 2.4710 0.4656 X3 0.0483 0.5250 X4 -0.0506 0.0403 ANOVA table Source SS df MS F Regression 2271423 b d Residual a C Total 2274122 26 (i) Write down the 'best fit' equation. [2 marks] (1i) What is the proportion of variation in operating cost that can be explained by the fitted equation in (i)? [2 marks] (iii) Test the significance of the overall model at 1% level of significance. [4 marks] (iv) Test whether machine hours has significant effect on operating cost at 5% level ific