10. What is the coefficient of determination (R2) for the data?Please put the answer in bold. AВspeciesIbrainMassInBrainMassgliaNeuronRatioHomo sapiens1373.37.221.65Pan troglodytes336.25.821.2Gorilla gorilla509.26.231.21Pongo pygmaeus342.75.840.98Hylobates muelleri101.84.621.22Papio anubis155.85.050.97Mandrillus sphinx159.25.071.02Macaca maura92.64.530.84Erythrocebus patasCercopithecus kandt102.34.631.0971.64.271.15Colobus angolensisTrachypithecus franAlouatta caraya74.44.311.291.24.511.1455.84.021.12Saimiri boliviensis24.13.180.51Aotus trivirgatus13.22.580.63Saguinus oedipus102.30.46Leontopithecus rosa12.22.50.6Pithecia pithecia303.40.64 Instructions Download the file "brain_metabolism.xlsx'. It contains data on brain mass in different species versus glia-neuron ratio, thelatter being a measurement of brain metabolism as the glia provides the metabolic needs of the neurons. The relationshipbetween THE LOGARITHM of the brain mass (in the third column) and Glia-neuron ratio (fourth column) appears linear and itis these two variables that we wish to analyze via linear regression. We would like to know if the human brain fits the trendfrom 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 andSSresidual 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 slope5. Calculate the predicted glia-neuron ratio for human brain given the human brain mass. Calculate the two confidenceintervals for the predicted glia-neuron ratio corresponding to the mass of the human brain: (i) the confidence interval for thepredicted 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)

What is the coefficient of determination (R2) for the data? The following data for the x and y…

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What is the coefficient of determination (R2) for the data? Please put the answer in bold.

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

10. What is the coefficient of determination (R²) for the data?

Please put the answer in bold.

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

Instructions Download the file "brain_metabolism.xlsx'. 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)

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