Blackbutt Architectural Premium Timbers harvest trees from their blackbutt plantations, and process these in response to orders they receive from builders for premium timber. The current process of selecting trees for harvest is wasteful. Sometimes they take more trees than they need, meaning that they miss out on extra growth opportunities for any tree prematurely harvested. Sometimes they dont take enough trees meaning they have to perform costly re-work. They need a way to easily predict the timber yield from a tree. A visiting expert suggests that they should be able to predict the yield from a tree by measuring its CBH (Circumference measured at Breast Height). To test this idea, they harvest and process a random sample of 29 trees. The data is captured in the table below. [Use Excel and show Excel work]

CBH	Yield
[centimeters]	[cubic meters]
93.5	0.341
241.2	5.184
273.1	5.590
194.0	3.301
346.8	11.748
115.9	3.307
334.0	8.826
349.3	8.582
167.4	4.267
312.7	9.136
252.1	6.934
96.0	1.682
125.5	2.290
120.7	3.123
150.9	10.253
331.4	7.981
237.5	6.780
334.1	7.477
340.7	9.246
340.5	10.484
285.4	6.265
217.4	4.118
111.7	1.634
95.6	1.679
121.5	2.361
188.3	3.693
233.3	4.024
315.3	9.875
327.3	10.061

a) Present this data as a fully labelled scattergram. The chart should include an informative caption. The chart should be created using Excel or a similar tool, and should include a trend line.

b) Inspection of the timber produced from the harvest reveals that one of the trees harvested was NOT a blackbutt tree, but another species with very different yield characteristics. From your scattergram in part (a) identify which point is most likely to correspond to this different tree. Explain what impact the inclusion of data for this tree would have had on the trendline that you included in your diagram.

c) Remove the point that you identified in part (b) from your data set. Using the remaining 28 data points, find the ordinary least squares (OLS) line of best fit that uses CBH to explain or predict tree yield. Provide an interpretation of the slope.

d) Determine and interpret the coefficient of determination.

e) Determine and interpret the standard error of the estimate. Explain how you could graphically sanity check your value for standard error of the estimate.

f) Use your regression equation to predict the yield of a blackbutt tree with a CBH of 400 centimeters. Explain why this prediction might be problematic

g) Briefly describe each of the LINE assumptions associated with performing a hypothesis test on the existence of a linear relationship. Test using alpha=5% whether the apparent linear relationship between CBH and Yield can be explained by chance and be careful to clearly state both your decision and your conclusion

h) Previous studies have established that for a closely related tree, the spotted gum, the predicted yield increases by 0.0298 cubic meters for each extra centimetre of CBH. Test using alpha=0.05 whether our slope for Blackbutt is significantly different to the slope for spotted gum. (Stretch question for stronger students)