a) Which of the following is(are) TRUE? 5 I. II. There is no need to test the significance of the individual regression coefficients. The variation in the weight that is explained by diameter at breast height, height of tree, and embryo type is 98.3% while the remaining percent is explained by other factors not considered in the model. i. ii. iii. iv. b) What is the conclusion if the regression coefficient of the variable diameter at breast height is tested? 6 i. I only II only Both I and II Neither I nor II ii. iii. iv. Weight of tree is dependent on diameter at breast height. Weight of tree is independent with diameter at breast height. Weight of tree is linearly dependent on diameter at breast height. Weight of tree is not linearly dependent on diameter at breast height.

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WILL UPVOTE, just pls help me answer the following questions in the attached image. Pls show complete solutions and explain them. Thank you!

3. It is beneficial to be able to estimate the weight of a tree based on
measurements of the tree taken before its harvest. Measurements on two
variables were taken from a random sample of trees, which were
subsequently harvested, and the actual weight (in kg) of the products
were determined. The variables measured are trunk diameter at breast
height or DBH (measured about 4 feet from ground level; in inches),
height of tree (in feet), and embryo type (monocot or dicot).
Suppose that the assumptions of linear regression were satisfied. A
multiple linear regression model for predicting the weight of tree using
diameter at breast height, height of tree, and embryo type was fitted. The
software output is summarized below. Use alpha=5%.
Intercept
DBH
height
type_monocot
Estimate
-1015.442
164.008
9.183
-161.278
Multiple R-squared
0.983
Std. Error
141.622
39.626
5.486
88.177
Adjusted R-squared
0.9703
tc
-7.170
4.139
1.674
-1.829
p-value
0.0020
0.0144
0.1695
0.1414
p-value (model)
0.0005383
a) Which of the following is(are) TRUE? 5
1.
II.
There is no need to test the significance of the individual regression coefficients.
The variation in the weight that is explained by diameter at breast height, height of tree, and
embryo type is 98.3% while the remaining percent is explained by other factors not considered in
the model.
i.
ii.
iii.
iv.
I only
i.
ii.
iii.
iv.
II only
Both I and II
Neither I nor II
b) What is the conclusion if the regression coefficient of the variable
diameter at breast height is tested? 6
Weight of tree is dependent on diameter at breast height.
Weight of tree is independent with diameter at breast height.
Weight of tree is linearly dependent on diameter at breast height.
Weight of tree is not linearly dependent on diameter at breast
height.
Transcribed Image Text:3. It is beneficial to be able to estimate the weight of a tree based on measurements of the tree taken before its harvest. Measurements on two variables were taken from a random sample of trees, which were subsequently harvested, and the actual weight (in kg) of the products were determined. The variables measured are trunk diameter at breast height or DBH (measured about 4 feet from ground level; in inches), height of tree (in feet), and embryo type (monocot or dicot). Suppose that the assumptions of linear regression were satisfied. A multiple linear regression model for predicting the weight of tree using diameter at breast height, height of tree, and embryo type was fitted. The software output is summarized below. Use alpha=5%. Intercept DBH height type_monocot Estimate -1015.442 164.008 9.183 -161.278 Multiple R-squared 0.983 Std. Error 141.622 39.626 5.486 88.177 Adjusted R-squared 0.9703 tc -7.170 4.139 1.674 -1.829 p-value 0.0020 0.0144 0.1695 0.1414 p-value (model) 0.0005383 a) Which of the following is(are) TRUE? 5 1. II. There is no need to test the significance of the individual regression coefficients. The variation in the weight that is explained by diameter at breast height, height of tree, and embryo type is 98.3% while the remaining percent is explained by other factors not considered in the model. i. ii. iii. iv. I only i. ii. iii. iv. II only Both I and II Neither I nor II b) What is the conclusion if the regression coefficient of the variable diameter at breast height is tested? 6 Weight of tree is dependent on diameter at breast height. Weight of tree is independent with diameter at breast height. Weight of tree is linearly dependent on diameter at breast height. Weight of tree is not linearly dependent on diameter at breast height.
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