Interpretation of coefficient of determination (R^2)

Question

[dominik.lagler]

I calculatet R^2 via the lm function in R. I examined how differences in my quantitative trait can be explained by differences in the diplotype effect (calculated via ASReml). It resulted in 0.58 for R^2. Or in case of the multiple linear regression (Diplotype effect, age, sex, body weight and height) 0.77. I would like to ask how to interpret these values in my discussion. How good are these values and how much i can trust them. Please advice me some good literature. Thanks in advance

[Renesh]

R-Squared (coefficient of determination) explains the variation in the y variable (response) that is explained by independent variables in the fitted regression. If your R-Squared is 0.58 for simple regression, it explains 58% of the variance in the response variable (quantitative trait) can be explained by the independent variable alone (diplotype effect).

In multiple regression, adjusted R-Squared (corrected for sample size and regression coefficients) is more appropriate than R-Squared as an increasing number of independent variables also increases R-Squared. Read more here about regression and interpretation

[dominik.lagler]

Thanks for your answer, i would like to hear your oppinion about the the values 0.58 and 0.77. Do you think they are good or high in that context?