# A 3D printer is used to produce devices. The printer can be run at variable speeds, but with an…

Question 3 (Bendigo) A 3D printer is used to produce devices. The printer can be run at variable

speeds, but with an increasing error rate as it runs faster. Three initial tests of the printer give the

following data:

error rate 5 5 8

speed 1 3 4

(a) • Draw a graph with ‘speed’ on the horizontal axis and ‘error rate’ on the vertical axis.

• Accurately mark the data points above on the graph.

• Draw an estimated a straight ‘line of best’ through these points of the form

error = a · speed + ß. You do not need to do any calculations, just estimate the height

and gradient of the line to produce a line of best fit.

• Clearly indicate the residuals on your graph.

• The graph should be roughly a quarter of a page in size.

(b) You then find out that the coefficient a is known to equal 2, for this kind of 3D printer, so

error = 2 · speed + ß.

(i) Using this value for a, solve for ß by minimising the sum of squares of the residuals using

a technique similar to that used in Reading 4.5. Clearly show each step of your working.

Note that your solution will not be given by the final equations in Reading 4.5, as the

value they produce for a 6= 2.

(ii) If you want the error rate to be as low as possible you can run the printer very slowly.

Use your solution for ß to explain the lowest error rate you expect.

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