title: Significant Quadratic terms - linear regression - R
body: <p>I'm given the following data:</p>
  
  <p><img src="https://i.stack.imgur.com/BIh1B.png" alt="enter image description here"></p>
  
  <p>I'm told to first fit the quadratic model.</p>
  
  <p><img src="https://i.stack.imgur.com/lHpNz.png" alt="enter image description here"></p>
  
  <pre><code> &gt; time = c(10,20,15,11,11,19,11,13,17,18,16,16,17,18,10)
   &gt; experience = c(24,1,10,15,17,3,20,9,3,1,7,9,7,5,20)
   &gt; fit = lm (time ~ experience + I(experience^2))
  &gt; summary(fit)
  
  Call:
  lm(formula = y ~ x + I(x^2))
  
  Residuals:
      Min      1Q  Median      3Q     Max 
  -1.8287 -0.8300  0.5054  0.7476  1.1713 
  
  Coefficients:
               Estimate Std. Error t value Pr(&gt;|t|)    
  (Intercept) 20.091108   0.724705  27.723    3e-12 ***
  x           -0.670522   0.154706  -4.334 0.000972 ***
  I(x^2)       0.009535   0.006326   1.507 0.157605    
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
  
  Residual standard error: 1.091 on 12 degrees of freedom
  Multiple R-squared:  0.9162,    Adjusted R-squared:  0.9022 
  F-statistic: 65.59 on 2 and 12 DF,  p-value: 3.465e-07
  </code></pre>
  
  <p>Everything seems fine there. </p>
  
  <p>My model is </p>
  
  <pre><code>y = 20.091-.671x+.0095x^2
  </code></pre>
  
  <p>Plotting it:</p>
  
  <pre><code>&gt; x = seq(0,25, by = .1)
  &gt; y = fit$coefficient[1]+fit$coefficient[2]*x+fit$coefficient[3]*x^2
  &gt; lines(x,y)
  </code></pre>
  
  <p><img src="https://i.stack.imgur.com/lLou6.png" alt="enter image description here"></p>
  
  <p>Again, everything seems fine.</p>
  
  <p>But then I'm told to test whether or not the quadratic term is significant at the a = .1 significance level. </p>
  
  <p>So I do</p>
  
  <pre><code>&gt; fit1 = lm (time ~ experience + I(experience^2))
  &gt; fit2 = lm(time~experience)
  &gt; anova(fit2, fit1)
  
  Analysis of Variance Table
  
  Model 1: time ~ experience
  Model 2: time ~ experience + I(experience^2)
    Res.Df    RSS Df Sum of Sq      F Pr(&gt;F)
  1     13 16.984                           
  2     12 14.280  1    2.7037 2.2719 0.1576
  </code></pre>
  
  <p>So my F value for the quadratic term is 2.27. Corresponding to a probability of .1576. .1576 > .1 therefore the quadratic term is significant at a = .1</p>
  
  <p>But my professor has indicated that we should find the quadratic term to be insignificant to our model. What am I doing wrong here?</p>