In dtkaplan/MultipleChoice: Support for Multiple Choice Questions in Shiny

if ( ! exists(".show_answers")) .show_answers <- TRUE

set.seed(3523)
As = runif(10,min=0,max=10)
Ds = 5 + 1.3*As + rnorm(length(As))
Ak = runif(14,min=10,max=20)
Dk = 27 - 1.3*Ak + rnorm(length(Ak))
gps = c(rep("S",length(As)), rep("K",length(Ak)))
df = data.frame( A = c(As,Ak), D = c(Ds,Dk), G = gps)
basic.plot = function(){
  plot( D ~ A, pch=gps, data=df, xlim=c(0,20), ylim=c(0,15))
}
# basic.plot()

. D --- a quantitative variable

. A --- a quantitative variable

. G --- a categorical variable with two levels: S & K

For each of the following, sketch a graph of the fitted model function of the indicated structure. Only a qualitative sketch is needed. (If you are doing this exercise on the internet, it will be good enough to draw out the graph on a piece of paper, roughly approximating the patterns of S and K seen in the graph. Then draw the model values right on your paper.)

An Example: `D ~ G`

basic.plot()
m1 = lm( D ~ 1, data=df, subset=G=="S")
h = coef(m1)[1]
lines( c(0,11),c(h,h), lwd=5)
m2 = lm( D ~ 1, data=df, subset=G=="K")
h = coef(m2)[1]
lines( c(9,20),c(h,h), lwd=5)

Draw these models:

a. D ~ A + G

basic.plot()
if (.show_answers) {
  m = lm( D ~ A+G, data=df)
  h = coef(m)
  lines( c(0,11), h[1] + h[3] + h[2]*c(0,11), lwd=5)
  lines( c(9,20), h[1] + h[2]*c(9,20), lwd=5)
}

b. D ~ A * G

basic.plot()
if (.show_answers) {
  m = lm( D ~ A*G, data=df)
  h = coef(m)
  lines( c(0,11), h[1] + h[3] + (h[2]+h[4])*c(0,11), lwd=5)
  lines( c(9,20), h[1] + h[2]*c(9,20), lwd=5)
}

c. D ~ A - 1

basic.plot()
if (.show_answers) {
  m = lm( D ~ A-1, data=df)
  h = coef(m)
  lines( c(0,9), h[1]*c(0,9), lwd=5)
  lines( c(11,20), h[1]*c(11,20), lwd=5)
}

d. D ~ 1

basic.plot()
if (.show_answers) {
  m = lm( D ~ 1, data=df)
  h = coef(m)
  lines( c(0,9), h[1] + 0 *c(0,9), lwd=5)
  lines( c(11,20), h[1] + 0*c(11,20), lwd=5)
}

e. D ~ A

basic.plot()
if (.show_answers) {
  m = lm( D ~ A, data=df)
  h = coef(m)
  lines( c(0,9), h[1] + h[2]*c(0,9), lwd=5)
  lines( c(11,20), h[1]+h[2]*c(11,20), lwd=5)
}

f. poly(A, 2)

basic.plot()
if (.show_answers) {
  m = lm( D ~ poly(A,2), data=df)
  xx = seq(0,20,length=100)
  yy = predict(m, newdata=list(A=xx))
  lines( xx, yy, lwd=5)
}