r-Squared Question



I am trying to undertand r-squared (the coefficient of determination)
of regression lines. If r, which is squared to obtain r-squared, is
the correlation between the predicted Y and the observed Y, then
doesn't that mean that any regression line whose predicted Y is a
perfect linear function of the observed Y has an r (and thus r-squared)
of 1?


Thanks,
Will


Keywords: r2 r^2 r**2 r-square r-squared rsquare rsquared

.



Relevant Pages

  • Re: Formula for Coefficient of Determination (Quadratic Regression)
    ... > For a linear regression it is simply given by R-square. ... Most statisticians consider that a linear regression because ... about using the term "coefficient of determination"? ...
    (sci.stat.edu)
  • Re: interpreting sign of t-value
    ... regression coefficient is equal to the hypothesized value. ... A negative t-value indicates the regression coefficient is LESS THAN the hypothesized value. ... Don't use t-test values to tell you about correlation. ...
    (sci.stat.math)
  • Re: Introducing a 3rd variable makes the correlation coefficient non-significant. Whats happenin
    ... This would be SIMPLE correlation coefficient between A and B. ... one independent variable -- that the regression coefficients are NO ... of http://groups.google.com and search for "Reef Fish" as author, ...
    (sci.stat.consult)
  • Re: R-squared in regression
    ... I don't also think that the regression-correlation distinction ... r as a sqrtin regression is misunderstood as the correlation ... correlation coefficient, which we're talking about here, is used for ...
    (sci.stat.consult)
  • Re: DETERMINATION MEASURE ?
    ... determination called the DETERMINATION MEASURE ". ... I came across this in a journal where a regression plot with a ... Equation A calculated by " Optimizing the equation by using ... citations of any of them. ...
    (sci.stat.math)