**Only answer G-J, I already did A-F** 2. Measuring the height of a California redwood tree...

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**Only answer G-J, I already did A-F**

2. Measuring the height of a California redwood tree is verydifficult because these trees grow to heights over 300 feet. Peoplefamiliar with these threes understand that the height of aCalifornia redwood tree is related to other characteristics of thetree, including the diameter of the tree at the breast height of aperson (in inches), the thickness of the bark of the tree (ininches), the distance from the closest neighboring tree (in yards),and the number of the other trees neighboring within 10 yards fromthe tree. Using the data set (Redwood.xlsx), conduct a regressionanalysis by answering the following questions.

Height
122.0
193.5
166.5
82.0
133.5
156.0
172.5
81.0
148.0
113.0
84.0
164.0
203.3
174.0
159.0
205.0
223.5
195.0
232.5
190.5
100.0
Diameter at breast height
20
36
18
10
21
29
51
11
26
12
13
40
52
30
22
42
45
54
39
36
8
Bark thickness
1.1
2.8
2.0
1.2
2.0
1.4
1.8
1.1
2.5
1.5
1.4
2.3
2.0
2.5
3.0
2.6
4.3
4.0
2.2
3.5
1.4
Distance from the closest
8.5
8.9
6.1
7.6
0.3
3.3
4.8
3.1
3.6
4.1
9.7
3.5
7.2
5.6
7.4
4.4
0.6
6.5
3.1
0.5
5.1
Trees within 10 yard
3
2
5
1
7
4
2
2
1
2
0
5
3
4
2
1
5
2
1
1
0

(g) Determine the coefficient of determination, ? 2 , andinterpret its meaning (f) At the level ? = 0.10, is there asignificant relationship between the thickness and the pressure?Answer based on the t test in the p-value approach

(h) Determine the adjusted coefficient of determination,adjusted ? 2 , and interpret its meaning

(i) Evaluate the linearity assumption using the residual plotabout the independent variable for diameter

(j) Evaluate the normality assumption using the normalprobability plot

Answer & Explanation Solved by verified expert
3.6 Ratings (632 Votes)

f) SUMMARY OUTPUT
Regression Statistics
Multiple R 0.890143976
R Square 0.792356299
Adjusted R Square 0.740445373
Standard Error 23.59964085
Observations 21
ANOVA
df SS MS F Significance F
Regression 4 34004.19695 8501.049236 15.26376757 2.53617E-05
Residual 16 8911.088769 556.943048
Total 20 42915.28571
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 66.53179445 22.53752929 2.952044725 0.009370562 18.75436668 114.3092222
Diameter at breast height 2.047792982 0.465597442 4.39820497 0.000448911 1.060770498 3.034815466
Bark thickness 14.59276252 7.718269335 1.890678063 0.076918199 -1.769237547 30.95476258
Distance from the closest -0.945471598 2.172038096 -0.435292364 0.669165076 -5.549986669 3.659043473
Trees within 10 yard 1.140592423 3.075882526 0.37081794 0.715636928 -5.379987243 7.661172089

g)

R^2 = 0.792356299

this means 79.24 % of variation in y is explained by this model

h) adjusted R^2 =   0.740445373

The adjusted R2 tells you the percentage of variation explained by only the independent variables that actually affect the dependent variable


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