Age	Species	Cones	Diameter	TASB
9	Loblolly	Yes	13.9	46.9
9	Loblolly	No	19.5	74.8
7	Loblolly	No	15.9	145.7
5	Loblolly	Yes	12.0	50.6
14	Loblolly	Yes	16.9	88.5
6	Loblolly	Yes	5.1	57.8
16	Loblolly	Yes	23.3	77.9
6	Loblolly	Yes	11.1	47.0
17	Loblolly	Yes	27.0	142.0
5	Loblolly	No	12.3	83.4
14	Loblolly	Yes	13.7	62.0
14	Loblolly	Yes	19.7	100.9
9	Loblolly	No	12.2	50.3
14	Loblolly	Yes	22.1	78.3
15	Loblolly	No	23.0	93.7
25	Loblolly	No	29.4	188.6
8	Loblolly	Yes	18.0	38.4
24	Loblolly	Yes	37.1	213.7
12	Loblolly	No	13.1	59.4
2	Loblolly	Yes	5.3	45.4
5	Slash	Yes	13.1	68.7
21	Slash	No	35.2	251.9
8	Slash	Yes	12.2	81.2
17	Slash	No	27.8	109.9
4	Slash	No	7.0	69.2
18	Slash	Yes	29.1	200.6
12	Slash	No	30.0	133.1
11	Slash	No	22.4	170.4
12	Slash	No	25.5	120.0
15	Slash	No	28.4	148.3
3	Slash	No	21.0	159.7
21	Slash	No	28.1	193.2
6	Slash	No	17.3	138.0
11	Slash	Yes	22.7	88.7
15	Slash	No	25.2	153.8
7	Slash	No	13.2	73.4
15	Slash	Yes	26.1	138.4
2	Slash	No	9.2	73.2
14	Slash	No	8.9	54.1
6	Slash	No	21.3	54.2
10	Slash	No	20.3	44.7
12	Slash	No	18.3	119.0
3	Slash	No	16.7	23.4
7	Slash	No	10.7	66.2
8	Slash	Yes	14.7	107.3
10	Slash	Yes	19.6	97.0
15	Slash	Yes	20.8	153.5

Pine trees have a significant commercial and ecological value in Australia. There is an increasing interest in measuring biomass of the pine trees. A forestry research institute collected data consisting of biomass measurements and other covariates for two species of pines, Loblolly and Slash. The data includes total tree above-stump biomass (TASB), diameter at 1.3 metres above ground, and the tree age. In addition, the researchers recorded whether or not each tree has been producing cones.

The data contains the following variables:

AgeAge of tree (years)

SpeciesTree species (Loblolly or Slash)

ConesProducing cones (Yes or No)

DiameterTree diameter at 1.3 m above ground (cm)

TASBTotal above-stump biomass (kg)

Question 1

The TASB is an example of a

nominal variable

discrete variable

continuous variable

categorical variable

Question 2

What proportion of pine trees have been producing cones?

0.426

0.447

0.553

0.574

Question 3

What is the observed number of loblolly trees producing cones?

12

13

20

27

Question 4

If there is no association between pine species and cone production, what is the expected count for the number of loblolly trees producing cones?

8.94

11.75

29.10

30.55

Question 5

What is the 2 statistic used to test for an association between pine species and cone production?

4.472

5.474

6.175

7.640

Question 6

Based on the statistic in Question 5, you can conclude that there is

moderate evidence to suggest that there is an association between pine species and cone production (p = 0.034)

weak evidence to suggest that there is an association between pine species and cone production (p = 0.083)

no evidence to suggest that there is an association between pine species and cone production (p = 0.581)

no evidence to suggest that there is an association between pine species and cone production (p = 0.966)

Question 7

The researchers want to determine whether pine trees that have been producing cones have a lower mean biomass and decide to use a Welch t-test to address this question. The result from this test suggests that there is

moderate evidence to suggest that mean biomass is lower for trees that have been producing cones (p = 0.038)

weak evidence to suggest that mean biomass is lower for trees that have been producing cones (p = 0.082)

no evidence to suggest that mean biomass is lower for trees that have been producing cones (p = 0.165)

no evidence to suggest that mean biomass is lower for trees that have been producing cones (p = 0.330)

Question 8

Which of the following is an assumption of the test in Question 7?

Linear relationship

Normal variability

Homogeneous variances

Equal standard deviations

Question 9

The researchers want to understand the relationship between biomass and tree age using a linear model. What is the slope of the least-squares line for the relationship between TASB and Age?

0.071 kg/year

3.699 kg/year

6.286 kg/year

33.492 kg/year

Question 10

Based on the least-squares line in Question 9, what is the estimated mean biomass of trees that are 9 years old?

4.34 kg

42.49 kg

56.57 kg

90.06 kg

Question 11

The researchers would like to extend this model to include the effects of tree diameter and species on biomass. What is the appropriate model they can use?

Multiple linear regression model

Two-way ANOVA model

Logistic regression model

One-way ANOVA model

Question 12

Based on the model in Question 11, you estimate that

holding the effect of age and diameter fixed, the mean biomass of slash pines is 19.820 kg higher than that of loblolly pines

holding the effect of age and diameter fixed, the mean biomass of slash pines is 27.220 kg higher than that of loblolly pines

holding the effect of age and diameter fixed, the mean biomass of slash pines is 27.220 kg lower than that of loblolly pines

holding the effect of age and diameter fixed, the mean biomass of slash pines is 19.820 kg lower than that of loblolly pines

Question 13

Based on the model in Question 11, the estimated mean biomass of loblolly pines that are 9 years old and have a diameter of 13.9 cm is

16.71 kg

36.53 kg

67.46 kg

87.28 kg

Question 14

Based on the model in Question 11, the residual for the first tree in the data is

-56.00 kg

-43.16 kg

-20.56 kg

10.37 kg

Question 15

Based on the model in Question 11, you can conclude that there is

strong evidence to suggest that there is an association between biomass and diameter, when holding the effects of tree species and age fixed (p = 0.002)

weak evidence to suggest that there is an association between biomass and diameter, when holding the effects of tree species and age fixed (p = 0.068)

weak evidence to suggest that there is an association between biomass and diameter, when holding the effects of tree species and age fixed (p = 0.089)

no evidence to suggest that there is an association between biomass and diameter, when holding the effects of tree species and age fixed (p = 0.368)

Question 16

A plot of residuals against fitted values for the model in Question 11 suggests that

the constant variance assumption is reasonable

the relationship between diameter and species is linear

the relationship between diameter and age is linear

the independence assumption is violated