有了一元回归为什么还要做多元回归

有了一元回归为什么还要做多元回归

同一个数据，同一个梦想？不一定。有人学了很久回归，却没有理解多元回归到底是要干嘛。> summary(lm(y ~ x)) Call: lm(formula = y ~ x) Residuals: Min 1Q Median 3Q Max -0.633978 -0.229549 -0.004557 0.208477 0.821191 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.65277 0.05837 11.184 < 2e-16 *** x 0.17580 0.02521 6.973 3.65e-10 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.294 on 98 degrees of freedom Multiple R-squared: 0.3316, Adjusted R-squared: 0.3248 F-statistic: 48.63 on 1 and 98 DF, p-value: 3.646e-10 > summary(lm(y ~ x + z)) Call: lm(formula = y ~ x + z) Residuals: Min 1Q Median 3Q Max -0.420562 -0.157195 0.008745 0.152034 0.432706 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.20056 0.06235 3.217 0.00176 ** x -0.68557 0.09013 -7.606 1.82e-11 *** z 0.72498 0.07433 9.753 4.57e-16 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.21 on 97 degrees of freedom Multiple R-squared: 0.6626, Adjusted R-squared: 0.6556 F-statistic: 95.23 on 2 and 97 DF, p-value: < 2.2e-16 数据来源：set.seed(711) x = seq(0,4, length =100) y =-x + jitter(rep(1:5, each =20),2) z = rep(1:5, each =20) par(mar = c(4,4,0.1,0.1)) plot(x, y) abline(lm(y ~ x), col ="red") plot(x, y, pch =20, col = z) lines(lowess(x, y, f =0.1), col ="red") summary(lm(y ~ x)) summary(lm(y ~ x + z))注意本例中局部平滑函数lowess()函数的应用。