# What conclusion can I draw from this R square?

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

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?

• As in [Explained Variance] 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. : wikiwand.com/en/Coefficient_of_determination – gunes Sep 12 '18 at 19:10
• Take a look at what happens when you take the log of both variables. – user2974951 Sep 13 '18 at 6:36

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). 