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http://people.sc.fsu.edu/~jburkardt/datasets/regression/x01.txt

  1. The data records the average weight of the brain and body for a number of mammal species. There are 62 rows of data.

  2. I have a task to take any two quantities that are related (min 10 data points is n=10)

  3. Derive regression equation, calculate R square

  4. Interpret your result

So to check if the two quantities are related I calculated chi-square which was 2648.193 which is higher than the critical value of 93.816 if we consider 0.005 significance level for a degree of freedom of 61.

Is this enough to say that these two quantities are related?

Also the equation of the trendline calculated using the below formula

  1. Y=bX+a

where b=(sum(XY)-nX̅Y̅)/sum(X^2)-n(X̅^2) and a=Ybar-b*Xbar

was

y = 0.9665x + 91.004 and R² = 0.8727

Here I am not able to interpret the result of R². Does it means the equation takes into account about 87.27% of the reason out of total reasons responsible for variability of y?

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    $\begingroup$ As in [Explained Variance][1] section, you're correct on your interpretation of $R^2$. The model can explain $87.27\%$ of the variability contained in $y$. As for the $\chi^2$ test, if your calculations are correct, yes it greatly exceeds the significance level; But, it is best to share how you did calculate your values here. [1]: wikiwand.com/en/Coefficient_of_determination $\endgroup$ – gunes Sep 12 '18 at 19:10
  • $\begingroup$ Take a look at what happens when you take the log of both variables. $\endgroup$ – user2974951 Sep 13 '18 at 6:36
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This is not intended as an answer, but I cannot include an image in a comment and so place it here. I found that a Gompertz type sigmoidal equation was a much better fit than a straight line, and to me makes more sense biologically. The equation is "y = a * exp(-exp(b - cx))" with parameters a = 5.6821373589805189E+03, b = 1.4154036478215724E+00, and c = 1.1917327717867921E-03 giving an R-squared of 0.9622 (see image). model

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  • $\begingroup$ This is a good example of overfitting a set of data. Indeed, what biological sense does it make to (a) predict body weight from brain weight and (b) assume there is an upper limit to body weight but none to brain weight?? $\endgroup$ – whuber Sep 12 '18 at 22:07
  • $\begingroup$ I will carefully consider what you have written. $\endgroup$ – James Phillips Sep 12 '18 at 22:15

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