Write down the equation of the regression line of y on x .

Use your regression line from part (a) as a model to answer the following.

Interpret the meaning of

(i)     the gradient;

(ii)    the y-intercept.

Estimate the cost of producing 60 boxes.

The factory sells the boxes for $19.99 each. Find the least number of boxes that the factory should produce in one day in order to make a profit.

Comment on the appropriateness of using your model to

(i)     estimate the cost of producing 5000 boxes;

(ii)    estimate the number of boxes produced when the total production cost is $540.

\(y = 10.7x + 121\)     A1A1     N2

[2 marks]

(i) additional cost per box (unit cost)     A1     N1

(ii) fixed costs     A1     N1

[2 marks]

attempt to substitute into regression equation     M1

e.g. \(y = 10.7 \times 60 + 121\) , \(y = 760.12 \ldots \)

\({\text{cost}} = \$ 760\) (accept \(\$ 763\) from 3 s.f. values)     A1    N2

[2 marks]

setting up inequality (accept equation)     M1

e.g. \(19.99x > 10.7x + 121\)

\(x > 12.94 \ldots \) A1

13 boxes (accept 14 from \(x > 13.02\) , using 3 s.f. values)     A1     N2

Note: Exception to the FT rule: if working shown, award the final A1 for a correct integer solution for their value of x.

[3 marks]

(i) this would be extrapolation, not appropriate     R1R1     N2

(ii) this regression line cannot predict x from y, not appropriate     R1R1     N2

[4 marks]