It contains data on brain mass in different species versus glia-neuron ratio, the latter being a measurement of brain metabolism as the glia provides the metabolic needs of the neurons.  The relationship between THE LOGARITHM of the brain mass (in the third column) and Glia-neuron ratio (fourth column) appears linear and it is these two variables that we wish to analyze via linear regression.  We would like to know if the human brain fits the trend from the other species.  Towards this end we will perform the regression on all species EXCEPT humans

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It contains data on brain mass in different species versus glia-neuron ratio, the latter being a measurement of brain metabolism as the glia provides the metabolic needs of the neurons.  The relationship between THE LOGARITHM of the brain mass (in the third column) and Glia-neuron ratio (fourth column) appears linear and it is these two variables that we wish to analyze via linear regression.  We would like to know if the human brain fits the trend from the other species.  Towards this end we will perform the regression on all species EXCEPT humans (Homo sapiens).  Again, throw out the human data from your analysis.  You will however need the human numbers for some of the questions.  The analysis to be performed is as follows:

1. Calculate the regression line (slope and intercept)

2. Perform an ANOVA test of the null hypothesis for zero slope.  From this analysis, obtain SStotal, SSregression and SSresidual as well as the corresponding MS statistics.

3. Perform a t-test of the null hypothesis of zero slope.

4. Compute a 95% confidence interval for the regression slope

5. Calculate the predicted glia-neuron ratio for human brain given the human brain mass.  Calculate the two confidence intervals for the predicted glia-neuron ratio corresponding to the mass of the human brain: (i) the confidence interval for the predicted mean and (ii) the confidence interval for a predicted individual.  

Once again:  You need the human data only for (5) above.  Throw it out for the analyses in (1)-(4)

 

Which 95% confidence interval for the predicted glia-neuron ratio should be used to test if human brains fit the trend observed for other species?

   

The 95% confidence interval for the mean glia-neuron ratio of all species, which have ln(brain mass) equal to that of humans.

   

The 95% confidence interval for the glia-neuron ratio of a randomly drawn species with a ln(brain mass) equal to that of humans.

 

 

Which of the following is a potential problem when assessing the fit of the human brain to the glia-neuron ratio versus ln(brain mass) trend observed in other species.

   

The brain masses are not normally distributed.

   

ln(brain mass) is not normally distributed.

   

We are performing extrapolation.

   

The co-efficient of determination (R2) is too low.

 

C.
D.
gliaNeuronRatio
7.22
brainMass
InBrainMass
species
1.65
1373.3
Homo sapiens
Pan troglodytes
Gorilla gorilla
336.2
5.82
1.2
509.2
6.23
1.21
342.7
5.84
0.98
Pongo pygmaeus
Hylobates muelleri
Papio anubis
Mandrillus sphinx
101.8
4.62
1.22
155.8
5.05
0.97
159.2
5.07
1.02
Macaca maura
92.6
4.53
0.84
102.3
4.63
1.09
Erythrocebus patas
Cercopithecus kandt
Colobus angolensis
71.6
4.27
1.15
74.4
4.31
1.2
1.14
Trachypithecus frant
1Alouatta caraya
91.2
4.51
55.8
4.02
1.12
24.1
3.18
0.51
5 Saimiri boliviensis
5 Aotus trivirgatus
7 Saguinus oedipus
8 Leontopithecus rosa
9 Pithecia pithecia
13.2
2.58
0.63
10
2.3
0.46
12.2
2.5
0.6
30
3.4
0.64
Transcribed Image Text:C. D. gliaNeuronRatio 7.22 brainMass InBrainMass species 1.65 1373.3 Homo sapiens Pan troglodytes Gorilla gorilla 336.2 5.82 1.2 509.2 6.23 1.21 342.7 5.84 0.98 Pongo pygmaeus Hylobates muelleri Papio anubis Mandrillus sphinx 101.8 4.62 1.22 155.8 5.05 0.97 159.2 5.07 1.02 Macaca maura 92.6 4.53 0.84 102.3 4.63 1.09 Erythrocebus patas Cercopithecus kandt Colobus angolensis 71.6 4.27 1.15 74.4 4.31 1.2 1.14 Trachypithecus frant 1Alouatta caraya 91.2 4.51 55.8 4.02 1.12 24.1 3.18 0.51 5 Saimiri boliviensis 5 Aotus trivirgatus 7 Saguinus oedipus 8 Leontopithecus rosa 9 Pithecia pithecia 13.2 2.58 0.63 10 2.3 0.46 12.2 2.5 0.6 30 3.4 0.64
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