Estimating R2 from a linear regression manually changing beta coefficient

Question

I want to know if there is a way to make a linear regression model and change the beta coefficient manually and estimate R2 after this change.

Simple example:

a <- c(2000 ,   2001  ,  2002  ,  2003 ,   2004)
b <- c(9.34 ,   8.50  ,  7.62  ,  6.93  ,  6.60)
c <- c(10.5 ,   12.8  ,  13.1  ,  14.4  ,  15.9)

fit=lm(a~b+c)
fit$coefficients
(Intercept)            b            c 
2005.1537642   -0.8948095    0.2866537 
summary(fit)$r.squared
[1] 0.9862912

I want to know what would be the R2 of this model if I used different betas for my variables "b" and "c".

Answer 1

You can calculate the coefficient of determination by taking the square of the sample correlation coefficient between the outcomes and their predicted values:

cor(a, -0.8948095 * b + 0.2866537 * c) ** 2
## [1] 0.9862912

Just replace the coefficients from your linear model with the coefficients that you want to test.