title: Making a scatterplot with PCA and how to read results
body: <p>Im a little newbie with R and not familiar with PCA. My problem is, from a survey I have a list with observations from nine variables, first one is the gender of the respondents, the next five (Q51_1_c,Q51_2_c,Q51_4_c,Q51_6_c,Q51_7_c) ask about entrepreneurial issues and the others ask about future expectations (Q56_1_c, Q56_2_c, Q56_3_c). Except gender, all this variables takes values between 1 and 5. I want to make a scatter plot with two axis. First one with "entrepreneurial variables" and second axis with "future expectations variables" and then define as points in the scatter plot the position of Male and Female. My data look like this:</p>
  
  <pre><code> x &lt;- "Q1b Q51_1_c Q51_2_c Q51_4_c Q51_6_c Q51_7_c Q56_1_c Q56_2_c Q56_3_c
  3    Male       5       4       4       4       4       5       4       4
  4  Female       4       3       4       4       3       3       4       3
  5  Female       1       1       1       1       1       3       1       1
  7  Female       2       1       1       1       1       5       1       4
  8  Female       4       4       5       4       4       5       4       4
  9  Female       3       3       4       4       3       3       4       4
  13   Male       4       4       4       4       5       3       3       3
  15 Female       3       4       4       4       4       1       1       5
  16 Female       4       1       4       4       4       3       3       3
  19 Female       3       2       3       3       3       3       3       3
  20   Male       1       1       1       1       1       3       1       5
  21 Female       3       1       1       2       1       3       3       3
  26 Female       5       5       1       2       1       4       4       3
  27 Female       2       1       1       1       1       1       1       1
  29   Male       2       2       2       2       1       4       4       4
  31 Female       3       1       1       1       1       5       2       3
  34 Female       4       1       1       4       3       3       1       4
  36 Female       5       1       1       4       4       5       1       2
  37   Male       5       1       2       4       4       5       4       5
  38 Female       3       1       1       1       1       1       1       1"
  </code></pre>
  
  <p>To run PCA this is my code:</p>
  
  <pre><code>x &lt;- na.omit(x) #Jus to simplyfy
  
  resul &lt;- prcomp(x[,-1], scale = TRUE)
  
  x$PC1 &lt;- resul$x[,1] #Saving Scores PC1
  x$PC2 &lt;- resul$x[,2] #Saving Scores PC2
  </code></pre>
  
  <p>The result axis are like this:</p>
  
  <pre><code>biplot(resul, scale = 0)
  </code></pre>
  
  <p><a href="https://i.stack.imgur.com/qPz4L.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/qPz4L.jpg" alt="enter image description here"></a></p>
  
  <p>Finally, to make the scatter plot:</p>
  
  <pre><code>x %&gt;%
    group_by(Q1b) %&gt;%
    summarise(mean_PC1 = mean(PC1),
              mean_PC2 = mean(PC2)) %&gt;%
      ggplot(aes(x=mean_PC1, y=mean_PC2, colour=Q1b)) +
      geom_point() +
      theme_bw()
  </code></pre>
  
  <p>Which gives me this: 
  <a href="https://i.stack.imgur.com/GBnCI.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/GBnCI.jpg" alt="enter image description here"></a></p>
  
  <p>I'm not sure how about read the results... Should I accept that Females in general get higher values in the dimension of future expectations than Males. And Males get higher values in the entrepreneurial dimension?</p>
  
  <p>Thanks in advance!!</p>