# 留学生辅导 Lab session4: Questions – cscodehelp代写

Lab session4: Questions
Question 1: Full Factorial 2k Designs
A typical golfer uses the putter for about 40% on strokes. Improving one¡¯s putting is a logical and perhaps simple way to improve a golf score. An experiment was conducted to study the effects of four factors on putting accuracy. The design factors are length of putt, type of putter, breaking putt versus straight putt, and level versus downhill putt. The response variable is distance from the ball to the centre of the cup after the ball comes to rest. One golfer performs the experiment, a 24 full factorial design with seven replicates was used, and all putts are made in random order. The results are shown in the next Table.
Length of putt (ft)

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Type of putter
Cavity back Cavity back Cavity back Cavity back Cavity back Cavity back Cavity back Cavity back
Break of putt
Straight Straight Straight Straight Breaking Breaking Breaking Breaking Straight Straight Straight Straight Breaking Breaking Breaking Breaking
Slope ofputt1234567
Level Level Level Level Level Level Level Level Downhill Downhill Downhill Downhill Downhill Downhill Downhill Downhill
10.0 18.0 14.0 12.5 0.0 16.5 4.5 17.5 4.0 6.0 1.0 14.5 0.0 10.0 34.0 11.0 0.0 0.0 18.5 19.5 5.0 20.5 18.0 20.0 6.5 18.5 7.5 6.0
16.5 4.5 0.0 23.5 4.5 18.0 14.5 10.0 19.5 18.0 16.0 5.5 15.0 16.0 8.5 0.0 41.5 39.0 6.5 3.5 8.0 4.5 6.5 10.0 21.5 10.5 6.5 0.0 0.0 0.0 0.0 4.5 18.0 5.0 7.0 10.0
19.0 16.0 18.5 20.5 17.5 33.0 12.0 14.0 5.0 25.5 21.5 0.0 16.0 15.0 11.0 29.5 19.0 10.0
0.0 10.0 0.0 8.0 8.0 8.0 0.0 17.5 6.0
10.0 7.0 36.0 0.5 9.0 3.0 7.0 8.5 36.0
13.0 41.0 14.0 15.5 24.0 16.0 1.0 4.0 6.5 32.5 18.5 8.0
(a)Analyse the data from this experiment by fitting an ANOVA model with intercept, main effects, and interactions of any order. Which of the main effects are significantly affect putting performance?
(b)Analyse the residuals from this experiment. Any indications of model inadequacy? Question 2: Fractional Factorial designs 2k-p
A replicated fractional factorial design is used to investigate the effect of five factors on the free height of leaf springs used in an automotive application. The factors are:
A = furnace temperature,
B = heating time,
Free Height
7.78 7.78 7.81 8.15 8.18 7.88 7.50 7.56 7.50 7.59 7.56 7.75 7.54 8.00 7.88 7.69 8.09 8.06 7.56 7.52 7.44 7.56 7.81 7.69 7.50 7.25 7.12 7.88 7.88 7.44 7.50 7.56 7.50 7.63 7.75 7.56 7.32 7.44 7.44 7.56 7.69 7.62 7.18 7.18 7.25
7.81 7.50 7.59
C = transfer time,
D = hold down time, and
E = quench oil temperature
The collected data are as shown here.
(a) Write out the alias structure for this design.
(b)What is the resolution of this design?
(c)Analyse the data using the 3 replications of this
experiment. What factors influence the free height?
(d)Analyse the data using the mean of the free height. What factors influence the mean free height?
– + – – – –
— — + + – -+ + -+ -+ + + + – – + — + + + + – + – + -+ + – +
+ – – – – – + –

(e) Analyse the residuals from this experiment (use the model from step c), and comment on your findings. (f) Based on the means of factors (main effects) and their interactions plots, what level of the coded
factors A, B, C, D and E would you recommend using to maximise the response?
(g)Is this the best possible design for five factors in 16 runs? Specifically, can you find a fractional design for five factors in 16 runs with a higher resolution than this one?