線性迴歸

R 中的 A/B 測試

Lauryn Burleigh

Data Scientist

最小平方法

殘差平方和
- 各點殘差平方後加總
最佳擬合線－最小平方和
誤差－均方誤差
- 平方和 / N

在 x 軸為 enjoyment、y 軸為 time 的正相關散佈圖上畫出最佳擬合線，紫色線段為各點殘差，左上角標示平方和公式。

線性迴歸模型

linear <- lm(Time ~ Enjoy, 
                data = Pizza) 
summary(linear)

Call:
lm(formula = Time ~ Enjoy, data = pizza)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.89270 -0.59857  0.04758  0.67764  2.12600 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  5.31964    0.19886  26.750  < 2e-16 ***
Enjoy        0.07707    0.01672   4.608 7.26e-06 ***

Residual standard error: 0.8947 on 198 degrees of freedom
Multiple R-squared:  0.09687,    
Adjusted R-squared:  0.09231 
F-statistic: 21.24 on 1 and 198 DF,  p-value: 7.262e-06

檢查假設

同方差性

變異量一致

plot(fitted(linear), resid(linear));
abline(0,0)

x 軸為模型擬合值、y 軸為殘差的散佈圖，y=0 處有一條水平線。

常態性

qqnorm(resid(linear));
qqline(resid(linear), col = "red")

Q-Q 圖：x 軸為殘差的理論分位數，y 軸為樣本分位數，並以紅色 45 度參考線顯示。

進行預測

Enjoy  <- 12
topredict <-  data.frame(Enjoy) 
predict(linear, newdata = topredict)

       1 
6.244452

Enjoy  <- c(12, 14)
topredict <-  data.frame(Enjoy) 
predict(linear, newdata = topredict)

       1        2 
6.244452 6.398587

納入群組

grplinear <- lm(Time ~ Enjoy + Topping,
                data = Pizza) 
summary(grplinear)

Enjoy  <- c(12, 14)
Topping <- "Cheese"
topredict <-  data.frame(Enjoy, Topping) 
predict(grplinear, newdata = topredict)

       1        2 
6.136022 6.269139

Call:
lm(formula = Time ~ Enjoy + Topping, 
data = pizza)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.87771 -0.51529  0.03993  0.68685  2.19460 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)       5.53891    0.24823  22.314  < 2e-16 ***
Enjoy             0.06656    0.01815   3.668 0.000315 ***
ToppingCheese -0.20159    0.13729  -1.468 0.143606

Residual standard error: 0.8921 on 197 degrees of freedom
Multiple R-squared:  0.1066,    
Adjusted R-squared:  0.09758 
F-statistic: 11.76 on 2 and 197 DF,  p-value: 1.499e-05

一起來練習吧！

R 中的 A/B 測試