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 Sresidual 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: (0 the confidence interval for the predicted mean and (i) 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)
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 Sresidual 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: (0 the confidence interval for the predicted mean and (i) 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)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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.
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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
What is the slope of the regression line (slope and intercept)
Please put the answer in bold.
Transcribed Image Text: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 (i) 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)
Transcribed Image Text:A
В
IbrainMass
species
Homo sapiens
InBrainMass
gliaNeuronRatio
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
Маcаcа maura
92.6
4.53
0.84
Erythrocebus patas
102.3
4.63
1.09
Cercopithecus kandt
71.6
4.27
1.15
Colobus angolensis
74.4
4.31
1.2
Trachypithecus fran
91.2
4.51
1.14
Alouatta caraya
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
Best estimate of the slope: SOP and Sum of square of X
E, (X; – X)(XY; – Y)
b
i=1
E, (X; – X,²
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