1. A researcher studied 32 giant pandas at a reserve. She recorded their daily b
ID: 3230247 • Letter: 1
Question
1. A researcher studied 32 giant pandas at a reserve. She recorded their daily bamboo intake (in kg), their height (in cm), and their sex (coded as female=0, male=1). She input her data into R in order to complete the GLM (regression) equation below:
a. Part of the output is given below. Fill in the empty boxes to determine if the main effects for height and sex are significant. For the p-value, please choose either “> .05” or “< .05.” (1pt)
lm(bamboo ~ height + sex + height*sex)
Estimate
Standard Error
t test statistic
p-value
Intercept
-7.101
2.189
-3.245
<.05
height
0.342
.022
sex
2.363
.419
height*sex
-0.023
.005
-4.600
<.05
Adjusted R2 = .5817
b. What is your overall regression equation? Be sure to include the variable names in your equation. (1.25pt)
c. What were her hypotheses? Be sure to list them all. (1.5pt)
d. The Adjusted R2 is .5817. What does this indicate? (0.75pt)
e. What is the coefficient (slope) for height? What does this number indicate in the context of the problem? (1pt)
f. What is the coefficient (slope) for sex? What does this number indicate in the context of the problem? (1pt)
g. Since the interaction is significant, the researcher will have to probe the results. Find the simple regression equation for males and the simple regression equation for females. (1pt)
h. Dazza Longbarrel works at a nature preserve that recently acquired a new giant panda. If the panda is an 80 cm tall male, how many kg of bamboo should Dazza expect to feed him each day? (0.5pt)
i. If Dazza Longbarrel’s giant panda actually eats 22kg of bamboo, what is that panda’s residual? (0.5pt)
Estimate
Standard Error
t test statistic
p-value
Intercept
-7.101
2.189
-3.245
<.05
height
0.342
.022
sex
2.363
.419
height*sex
-0.023
.005
-4.600
<.05
Explanation / Answer
a)
t-test-height=0.342/0.022=15.55
t-test-sex=2.363/0.419=5.64
b)
Bamboo intake=-7.101+0.342(height)+2.363(sex)-0.023(height*sex)
c)
H0=B1=B2=B3=0
H1#B1=B2=B3=0
d)
58.17% of the variation in bamboo intake is explained by height, sex and height*sex taking into account the sample size and number of independent variables.
e)
The coefficient for height is 0.342. This means that bamboo intake would go up by 0.342 for every 1 unit increase in height, all other factors remaining constant.
f)
The coefficient for sex is 2.363. This means that bamboo intake would go up by 2.363 for every 1 unit increase in height, all other factors remaining constant.
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