Interaction between variables

Y = β_{0}^{} + β_{1}^{} X_{}^{} + β_{2}^{} X_{}^{2} + β_{3}^{} Z_{}^{} + β_{4}^{} X_{}^{} Z_{}^{} + β_{5}^{} X_{}^{2} Z_{}^{} + ε

library(ggplot2)

XLineA <- runif(numbervalues, 0, 20);          # Simulates X-data 0 - 20,
XLineB <- runif(numbervalues, 0, 20);          # from uniform distribution.
    
YLineA <- LineA_B0 + LineA_B1*XLineA + LineA_B2*XLineA*XLineA + rnorm(numbervalues, 0, standres)
YLineB <- LineB_B0 + LineB_B1*XLineB + LineB_B2*XLineB*XLineB + rnorm(numbervalues, 0, standres)

type  = rep(c("A", "B"), each = numbervalues)
    
Ytot <- c(YLineA, YLineB)                  # All Y-data.
Xtot <- c(XLineA, XLineB)                  # All X-data.
    
myData <- data.frame(Ytot, Xtot, type)
         
model <- lm(Ytot ~ (Xtot + I(Xtot*Xtot))*type )

summary(model)                                         # Shows result from analysis.
residuals <- resid(model)                              # Shows the residuals.
myData['Residuals'] <- residuals                       # Includes residuals into data frame.
   
mat_coeff <- summary(model)$coefficients               # All estimated coefficients.

b0 <- mat_coeff[1, 1]   # (Intercept)                  # Extracts coefficients.
b1 <- mat_coeff[2, 1]   # X
b2 <- mat_coeff[3, 1]   # X2
b3 <- mat_coeff[4, 1]   # typeB
b4 <- mat_coeff[5, 1]   # X:typeB
b5 <- mat_coeff[6, 1]   # X2:typeB 
 
b0A <- b0                                              # ESTIMATED intercept and slope (red)
b1A <- b1
b2A <- b2

b0B <- b0 + b3                                         # ESTIMATED intercept and slope (blue)
b1B <- b1 + b4
b2B <- b2 + b5

ymax = max(1.05*Ytot)                                  # Stretches the Y-axis.
ymin = min(Ytot)

fun1 <- function(XLineA) b0A + b1A*XLineA + b2A*XLineA*XLineA 
fun2 <- function(XLineB) b0B + b1B*XLineB + b2B*XLineB*XLineB

myDiagram <- ggplot(myData, aes(x = Xtot, y = Ytot)) +
  annotate("text", x=10.0, y=ymax, label="Estimated models", fontface="bold", color="blue", size=6) + 
  geom_point(colour=rep(c("red","blue"), each=numbervalues)) + ylim(ymin, ymax)
  
myDiagram <- myDiagram + stat_function(fun = fun1, color="red")              # Adds line (A)
myDiagram <- myDiagram + stat_function(fun = fun2, color="blue")             # Adds line (B)
myDiagram

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47. Interaction between variables

A linear model with one X-variable and one group variable (Z)

The data column consists of two groups,
possibly from different models

Här skall skrivas infotext.

Data consists of two groups (A) and
(B) generated by the models:

β₀

β₁

β₂

More regression (Sw)

3D-graphs (Eng)

t-test (Sw)