Simple linear regression

Machine Learning for Marketing Analytics in R

Verena Pflieger

Data Scientist at INWT Statistics

simpleLM <- lm(futureMargin ~ margin, data = clvData1)
summary(simpleLM)

Call:
lm(formula = futureMargin ~ margin, data = clvData1)
Residuals:
    Min      1Q  Median      3Q     Max 
-56.055  -9.258   0.727  10.060  49.869 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 12.63068    0.49374   25.58   <2e-16 ***
margin       0.64543    0.01467   43.98   <2e-16 ***

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 14.24 on 4189 degrees of freedom
Multiple R-squared:  0.3159,    Adjusted R-squared:  0.3158 
F-statistic:  1935 on 1 and 4189 DF,  p-value: < 2.2e-16

ggplot(clvData1, aes(margin, futureMargin)) +
  geom_point() +
  geom_smooth(method = lm, se = FALSE) +
  xlab("Margin year 1") +
  ylab("Margin year 2")

Assumptions of Simple Linear Regression Model

Linear relationship between x and y
No measurement error in x (weak exogeneity)
Independence of errors
Expectation of errors is 0
Constant variance of prediction errors (homoscedasticity)
Normality of errors

Time to practice!

Machine Learning for Marketing Analytics in R