Question

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

2. Measuring the height of a California redwood tree is very difficult because these trees grow to heights over 300 feet. People familiar with these threes understand that the height of a California redwood tree is related to other characteristics of the tree, including the diameter of the tree at the breast height of a person (in inches), the thickness of the bark of the tree (in inches), the distance from the closest neighboring tree (in yards), and the number of the other trees neighboring within 10 yards from the tree. Using the data set (Redwood.xlsx), conduct a regression analysis 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 , and interpret its meaning (f) At the level ? = 0.10, is there a significant 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 plot about the independent variable for diameter

(j) Evaluate the normality assumption using the normal probability plot

Answer 1

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