Question

In: Statistics and Probability

Height Diameter at breast height 122.0 20 193.5 36 166.5 18 82.0 10 133.5 21 156.0...

Height	Diameter at breast height
122.0	20
193.5	36
166.5	18
82.0	10
133.5	21
156.0	29
172.5	51
81.0	11
148.0	26
113.0	12
84.0	13
164.0	40
203.3	52
174.0	30
159.0	22
205.0	42
223.5	45
195.0	54
232.5	39
190.5	36
100.0	8

Measuring the height of a California redwood tree is very difficult because these trees grow to heights of over 300 feet. People familiar with these trees understand that the height of the tree is related to other characteristics of the tree, such as the diameter of the tree at the breast height of a person. In the Excel data file for this assignment, under the tab Redwood, is a random sample of 21 redwood trees including the height (in feet) and the diameter (in inches) at breast height.

a. Create the appropriate scatter plot and calculate the coefficient of correlation. Comment on the results. Does it appear a linear relationship exists?

b. Use the least-squares method to compute the regression coefficients b₀ and b₁.

c. Interpret the meaning of b₀ and b₁ in this problem.

d. What if the predicted mean height for a tree that has a breast height diameter of 25 inches? 60 inches?

e. Determine the coefficient of determination, R², and explain its meaning in this problem.

g. Perform a complete residual analysis. Does the analysis support all the assumptions required for a valid model? Explain.

h. Create the 95% confidence interval and the 95% prediction interval for a tree with a diameter of 25”. Interpret your results.

h. What conclusions can you reach about the relationship between the diameter of the tree and its height?

Solutions

Expert Solution

Solution : ( a )

X	Y	*X Y**	*X X**	*Y Y**
122.0	20	2440	14884	400
193.5	36	6966	37442.25	1296
166.5	18	2997	27722.25	324
82.0	10	820	6724	100
133.5	21	2803.5	17822.25	441
156.0	29	4524	24336	841
172.5	51	8797.5	29756.25	2601
81.0	11	891	6561	121
148.0	26	3848	21904	676
113.0	12	1356	12769	144
84.0	13	1092	7056	169
164.0	40	6560	26896	1600
203.3	52	10571.6	41330.89	2704
174.0	30	5220	30276	900
159.0	22	3498	25281	484
205.0	42	8610	42025	1764
223.5	45	10057.5	49952.25	2025
195.0	54	10530	38025	2916
232.5	39	9067.5	54056.25	1521
190.5	36	6858	36290.25	1296
100.0	8	800	10000	64

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Solution : ( e )

orchestra answered 1 year ago

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