title: How to create prediction line for Quadratic Model
body: <p>I am trying to create a quadratic prediction line for a quadratic model. I am using the Auto dataset that comes with R. I had no trouble creating the prediction line for a linear model. However, the quadratic model yields crazy looking lines. Here is my code. </p>
  
  <pre><code># Linear Model
  plot(Auto$horsepower, Auto$mpg,
       main = "MPG versus Horsepower",
       pch = 20)
  
  lin_mod = lm(mpg ~ horsepower,
               data = Auto)
  lin_pred = predict(lin_mod)
  
  
  lines(
    Auto$horsepower, lin_pred,
    col = "blue", lwd = 2
  )
  
  
  # The Quadratic model
  Auto$horsepower2 = Auto$horsepower^2
  quad_model = lm(mpg ~ horsepower2,
                  data = Auto)
  quad_pred = predict(quad_model)
  
  lines(
    Auto$horsepower,
    quad_pred,
    col = "red", lwd = 2
  )
  </code></pre>
  
  <p>I am 99% sure that the issue is the prediction function. Why can't I produce a neat looking quadratic prediction curve? The following code I tried does not work—could it be related?: </p>
  
  <pre><code>quad_pred = predict(quad_model, data.frame(horsepower = Auto$horsepower))
  </code></pre>
  
  <p>Thanks!</p>