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# Computation of R-squared with lm() in R

Confusion on difference between the $$R^2$$ results from the lm() function in R and from the Equation

$$1-rss/sst$$ (1)

z1 = c(0.603,0.643,0.603,0.643,0.643,0.603,0.601,0.641,0.601,0.603,0.601,0.641,0.643,0.641,0.641,0.601,0.622)
z2 = c(0.38,0.34,0.38,0.34,0.34,0.38,0.38,0.34,0.38,0.38,0.38,0.34,0.34,0.34,0.34,0.38,0.36)
z3= c(0.017,0.017,0.017,0.017,0.017,0.017,0.019,0.019,0.019,0.017,0.019,0.019,0.017,0.019,0.019,0.019,0.018)
z4= c(0.503505,0.536905,0.503505,0.536905,0.581915,0.545715,0.501835,0.535235,0.501835,0.545715,0.543905 ,0.535235,0.581915,0.580105,0.580105,0.543905,0.541140)
z5 = c(0.3420,0.3060,0.3724,0.3332,0.3060,0.3420,0.3420,0.3060,0.3724,0.3724,0.3420,0.3332,0.3332,0.3060,0.3332,0.3724,0.3384)
z = data.frame(z1,z2,z3,z4,z5)
y = c(35.040, 32.100, 37.800, 33.300, 31.320, 34.026, 34.140, 31.968, 36.990, 35.970, 33.870, 33.438, 33.144, 32.106, 33.660, 35.520, 33.438)

fit = lm(y ~ z1 + z2 + z3 + z4 + z5 - 1, data = data.frame(y, z))

e = fit$residuals rss = sum(e^2) sst = sum((y-mean(y))^2) 1-rss/sst  [1] 0.9305206 summary(fit)$r.squared


0.9998195

I also checked anova(fit). I think the $$R^2$$ results from summary(fit)$r.squared is correct. But why is the computation from Equation (1) wrong? # Computation of R-squared with lm in R Confusion on difference between the $$R^2$$ results from the lm() function in R and from the Equation $$1-rss/sst$$ (1) z1 = c(0.603,0.643,0.603,0.643,0.643,0.603,0.601,0.641,0.601,0.603,0.601,0.641,0.643,0.641,0.641,0.601,0.622) z2 = c(0.38,0.34,0.38,0.34,0.34,0.38,0.38,0.34,0.38,0.38,0.38,0.34,0.34,0.34,0.34,0.38,0.36) z3= c(0.017,0.017,0.017,0.017,0.017,0.017,0.019,0.019,0.019,0.017,0.019,0.019,0.017,0.019,0.019,0.019,0.018) z4= c(0.503505,0.536905,0.503505,0.536905,0.581915,0.545715,0.501835,0.535235,0.501835,0.545715,0.543905 ,0.535235,0.581915,0.580105,0.580105,0.543905,0.541140) z5 = c(0.3420,0.3060,0.3724,0.3332,0.3060,0.3420,0.3420,0.3060,0.3724,0.3724,0.3420,0.3332,0.3332,0.3060,0.3332,0.3724,0.3384) z = data.frame(z1,z2,z3,z4,z5) y = c(35.040, 32.100, 37.800, 33.300, 31.320, 34.026, 34.140, 31.968, 36.990, 35.970, 33.870, 33.438, 33.144, 32.106, 33.660, 35.520, 33.438) fit = lm(y ~ z1 + z2 + z3 + z4 + z5 - 1, data = data.frame(y, z)) e = fit$residuals
sst = sum((y-mean(y))^2)


[1] 0.9305206

summary(fit)$r.squared  0.9998195 I also checked anova(fit). I think the $$R^2$$ results from summary(fit)$r.squared is correct. But why is the computation from Equation (1) wrong?

# Computation of R-squared with lm() in R

Confusion on difference between the $$R^2$$ results from the lm() function in R and from the Equation

$$1-rss/sst$$ (1)

z1 = c(0.603,0.643,0.603,0.643,0.643,0.603,0.601,0.641,0.601,0.603,0.601,0.641,0.643,0.641,0.641,0.601,0.622)
z2 = c(0.38,0.34,0.38,0.34,0.34,0.38,0.38,0.34,0.38,0.38,0.38,0.34,0.34,0.34,0.34,0.38,0.36)
z3= c(0.017,0.017,0.017,0.017,0.017,0.017,0.019,0.019,0.019,0.017,0.019,0.019,0.017,0.019,0.019,0.019,0.018)
z4= c(0.503505,0.536905,0.503505,0.536905,0.581915,0.545715,0.501835,0.535235,0.501835,0.545715,0.543905 ,0.535235,0.581915,0.580105,0.580105,0.543905,0.541140)
z5 = c(0.3420,0.3060,0.3724,0.3332,0.3060,0.3420,0.3420,0.3060,0.3724,0.3724,0.3420,0.3332,0.3332,0.3060,0.3332,0.3724,0.3384)
z = data.frame(z1,z2,z3,z4,z5)
y = c(35.040, 32.100, 37.800, 33.300, 31.320, 34.026, 34.140, 31.968, 36.990, 35.970, 33.870, 33.438, 33.144, 32.106, 33.660, 35.520, 33.438)

fit = lm(y ~ z1 + z2 + z3 + z4 + z5 - 1, data = data.frame(y, z))

e = fit$residuals rss = sum(e^2) sst = sum((y-mean(y))^2) 1-rss/sst  0.9305206 summary(fit)$r.squared


0.9998195

I also checked anova(fit). I think the $$R^2$$ results from summary(fit)$r.squared is correct. But why is the computation from Equation (1) wrong? 4 added 5 characters in body Confusion on difference between the $$R^2$$ results from the lm() function in R and from the Equation $$1-rss/sst$$ (1) z1 = c(0.603,0.643,0.603,0.643,0.643,0.603,0.601,0.641,0.601,0.603,0.601,0.641,0.643,0.641,0.641,0.601,0.622) z2 = c(0.38,0.34,0.38,0.34,0.34,0.38,0.38,0.34,0.38,0.38,0.38,0.34,0.34,0.34,0.34,0.38,0.36) z3= c(0.017,0.017,0.017,0.017,0.017,0.017,0.019,0.019,0.019,0.017,0.019,0.019,0.017,0.019,0.019,0.019,0.018) z4= c(0.503505,0.536905,0.503505,0.536905,0.581915,0.545715,0.501835,0.535235,0.501835,0.545715,0.543905 ,0.535235,0.581915,0.580105,0.580105,0.543905,0.541140) z5 = c(0.3420,0.3060,0.3724,0.3332,0.3060,0.3420,0.3420,0.3060,0.3724,0.3724,0.3420,0.3332,0.3332,0.3060,0.3332,0.3724,0.3384) z = data.frame(z1,z2,z3,z4,z5) y = c(35.040, 32.100, 37.800, 33.300, 31.320, 34.026, 34.140, 31.968, 36.990, 35.970, 33.870, 33.438, 33.144, 32.106, 33.660, 35.520, 33.438) fit = lm(y ~ z1 + z2 + z3 + z4 + z5 - 1, data = data.frame(y, z)) e = fit$residuals
sst = sum((y-mean(y))^2)


[1] 0.9305206

summary(fit)$r.squared  0.9998195 I also checked r anova(fit). I think the $$R^2$$ results from summary(fit)$r.squared is correct. But why is the computation from Equation (1) wrong?

Confusion on difference between the $$R^2$$ results from the lm() function in R and the Equation

$$1-rss/sst$$ (1)

z1 = c(0.603,0.643,0.603,0.643,0.643,0.603,0.601,0.641,0.601,0.603,0.601,0.641,0.643,0.641,0.641,0.601,0.622)
z2 = c(0.38,0.34,0.38,0.34,0.34,0.38,0.38,0.34,0.38,0.38,0.38,0.34,0.34,0.34,0.34,0.38,0.36)
z3= c(0.017,0.017,0.017,0.017,0.017,0.017,0.019,0.019,0.019,0.017,0.019,0.019,0.017,0.019,0.019,0.019,0.018)
z4= c(0.503505,0.536905,0.503505,0.536905,0.581915,0.545715,0.501835,0.535235,0.501835,0.545715,0.543905 ,0.535235,0.581915,0.580105,0.580105,0.543905,0.541140)
z5 = c(0.3420,0.3060,0.3724,0.3332,0.3060,0.3420,0.3420,0.3060,0.3724,0.3724,0.3420,0.3332,0.3332,0.3060,0.3332,0.3724,0.3384)
z = data.frame(z1,z2,z3,z4,z5)
y = c(35.040, 32.100, 37.800, 33.300, 31.320, 34.026, 34.140, 31.968, 36.990, 35.970, 33.870, 33.438, 33.144, 32.106, 33.660, 35.520, 33.438)

fit = lm(y ~ z1 + z2 + z3 + z4 + z5 - 1, data = data.frame(y, z))

e = fit$residuals rss = sum(e^2) sst = sum((y-mean(y))^2) 1-rss/sst  [1] 0.9305206 summary(fit)$r.squared


0.9998195

I also checked r anova(fit). I think the $$R^2$$ results from summary(fit)$r.squared is correct. But why is the computation from Equation (1) wrong? Confusion on difference between the $$R^2$$ results from the lm() function in R and from the Equation $$1-rss/sst$$ (1) z1 = c(0.603,0.643,0.603,0.643,0.643,0.603,0.601,0.641,0.601,0.603,0.601,0.641,0.643,0.641,0.641,0.601,0.622) z2 = c(0.38,0.34,0.38,0.34,0.34,0.38,0.38,0.34,0.38,0.38,0.38,0.34,0.34,0.34,0.34,0.38,0.36) z3= c(0.017,0.017,0.017,0.017,0.017,0.017,0.019,0.019,0.019,0.017,0.019,0.019,0.017,0.019,0.019,0.019,0.018) z4= c(0.503505,0.536905,0.503505,0.536905,0.581915,0.545715,0.501835,0.535235,0.501835,0.545715,0.543905 ,0.535235,0.581915,0.580105,0.580105,0.543905,0.541140) z5 = c(0.3420,0.3060,0.3724,0.3332,0.3060,0.3420,0.3420,0.3060,0.3724,0.3724,0.3420,0.3332,0.3332,0.3060,0.3332,0.3724,0.3384) z = data.frame(z1,z2,z3,z4,z5) y = c(35.040, 32.100, 37.800, 33.300, 31.320, 34.026, 34.140, 31.968, 36.990, 35.970, 33.870, 33.438, 33.144, 32.106, 33.660, 35.520, 33.438) fit = lm(y ~ z1 + z2 + z3 + z4 + z5 - 1, data = data.frame(y, z)) e = fit$residuals
sst = sum((y-mean(y))^2)


[1] 0.9305206

summary(fit)$r.squared  0.9998195 I also checked anova(fit). I think the $$R^2$$ results from summary(fit)$r.squared is correct. But why is the computation from Equation (1) wrong?

3 improved formatting

Confusion on difference between the R2$$R^2$$ results from the lmlm() function in R and the Equation

1-rss/sst$$1-rss/sst$$ (1)

z1 = c(0.603,0.643,0.603,0.643,0.643,0.603,0.601,0.641,0.601,0.603,0.601,0.641,0.643,0.641,0.641,0.601,0.622)
z2 = c(0.38,0.34,0.38,0.34,0.34,0.38,0.38,0.34,0.38,0.38,0.38,0.34,0.34,0.34,0.34,0.38,0.36)
z3= c(0.017,0.017,0.017,0.017,0.017,0.017,0.019,0.019,0.019,0.017,0.019,0.019,0.017,0.019,0.019,0.019,0.018)
z4= c(0.503505,0.536905,0.503505,0.536905,0.581915,0.545715,0.501835,0.535235,0.501835,0.545715,0.543905 ,0.535235,0.581915,0.580105,0.580105,0.543905,0.541140)
z5 = c(0.3420,0.3060,0.3724,0.3332,0.3060,0.3420,0.3420,0.3060,0.3724,0.3724,0.3420,0.3332,0.3332,0.3060,0.3332,0.3724,0.3384)
z = data.frame(z1,z2,z3,z4,z5)
y = c(35.040, 32.100, 37.800, 33.300, 31.320, 34.026, 34.140, 31.968, 36.990, 35.970, 33.870, 33.438, 33.144, 32.106, 33.660, 35.520, 33.438)

fit = lm(y~z1+z2+z3+z4+z5y ~ z1 + z2 + z3 + z4 + z5 - 1, data = data.frame(y, z))

e = fit$residuals rss = sum(e^2) sst = sum((y-mean(y))^2) 1-rss/sst  [1] 0.9305206 summary(fit)$r.squared


0.9998195

I also checked r anova(fit). I think the R2$$R^2$$ results from the summary(fit)$r.squared is correct. But why is the computation from the Equation (1) wrong? Confusion on difference between the R2 results from the lm function in R and the Equation 1-rss/sst (1) z1 = c(0.603,0.643,0.603,0.643,0.643,0.603,0.601,0.641,0.601,0.603,0.601,0.641,0.643,0.641,0.641,0.601,0.622) z2 = c(0.38,0.34,0.38,0.34,0.34,0.38,0.38,0.34,0.38,0.38,0.38,0.34,0.34,0.34,0.34,0.38,0.36) z3= c(0.017,0.017,0.017,0.017,0.017,0.017,0.019,0.019,0.019,0.017,0.019,0.019,0.017,0.019,0.019,0.019,0.018) z4= c(0.503505,0.536905,0.503505,0.536905,0.581915,0.545715,0.501835,0.535235,0.501835,0.545715,0.543905 ,0.535235,0.581915,0.580105,0.580105,0.543905,0.541140) z5 = c(0.3420,0.3060,0.3724,0.3332,0.3060,0.3420,0.3420,0.3060,0.3724,0.3724,0.3420,0.3332,0.3332,0.3060,0.3332,0.3724,0.3384) z = data.frame(z1,z2,z3,z4,z5) y = c(35.040, 32.100, 37.800, 33.300, 31.320, 34.026, 34.140, 31.968, 36.990, 35.970, 33.870, 33.438, 33.144, 32.106, 33.660, 35.520, 33.438) fit = lm(y~z1+z2+z3+z4+z5-1, data = data.frame(y, z)) e = fit$residuals
sst = sum((y-mean(y))^2)


[1] 0.9305206

summary(fit)$r.squared  0.9998195 I also checked anova(fit). I think the R2 results from the summary(fit)$r.squared is correct. But why is the computation from the Equation (1) wrong?

Confusion on difference between the $$R^2$$ results from the lm() function in R and the Equation

$$1-rss/sst$$ (1)

z1 = c(0.603,0.643,0.603,0.643,0.643,0.603,0.601,0.641,0.601,0.603,0.601,0.641,0.643,0.641,0.641,0.601,0.622)
z2 = c(0.38,0.34,0.38,0.34,0.34,0.38,0.38,0.34,0.38,0.38,0.38,0.34,0.34,0.34,0.34,0.38,0.36)
z3= c(0.017,0.017,0.017,0.017,0.017,0.017,0.019,0.019,0.019,0.017,0.019,0.019,0.017,0.019,0.019,0.019,0.018)
z4= c(0.503505,0.536905,0.503505,0.536905,0.581915,0.545715,0.501835,0.535235,0.501835,0.545715,0.543905 ,0.535235,0.581915,0.580105,0.580105,0.543905,0.541140)
z5 = c(0.3420,0.3060,0.3724,0.3332,0.3060,0.3420,0.3420,0.3060,0.3724,0.3724,0.3420,0.3332,0.3332,0.3060,0.3332,0.3724,0.3384)
z = data.frame(z1,z2,z3,z4,z5)
y = c(35.040, 32.100, 37.800, 33.300, 31.320, 34.026, 34.140, 31.968, 36.990, 35.970, 33.870, 33.438, 33.144, 32.106, 33.660, 35.520, 33.438)

fit = lm(y ~ z1 + z2 + z3 + z4 + z5 - 1, data = data.frame(y, z))

e = fit$residuals rss = sum(e^2) sst = sum((y-mean(y))^2) 1-rss/sst  [1] 0.9305206 summary(fit)$r.squared


0.9998195

I also checked r anova(fit). I think the $$R^2$$ results from summary(fit)\$r.squared is correct. But why is the computation from Equation (1) wrong?

2 added 75 characters in body
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