diff --git a/labs/04_machine-learning/04_PCA-analysis_key.ipynb b/labs/04_machine-learning/04_PCA-analysis_key.ipynb
index d05919f..4c53975 100644
--- a/labs/04_machine-learning/04_PCA-analysis_key.ipynb
+++ b/labs/04_machine-learning/04_PCA-analysis_key.ipynb
@@ -28,7 +28,7 @@
    "metadata": {},
    "source": [
     "## Protein structures\n",
-    "+ Write a function that loads in the `x`, `y`, and `z` coordinates for all `CA` atoms from a pdb file."
+    "+ Write a function that loads in the `x`, `y`, and `z` coordinates for all `CA` atoms from a pdb file and returns all the coordinates in an numpy array. (Hint: the shape of this array should be (number-of-`CA`-atoms, 3).)"
    ]
   },
   {
@@ -64,9 +64,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "hm1 = load_pdb(\"homolog-1.pdb\")\n",
@@ -83,9 +81,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "plt.plot(hm1[:,0],hm1[:,1])\n",
@@ -120,15 +116,13 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "+ Plot the transformed coordinates on top of one another."
+    "+ Plot the first 2 transformed coordinates on top of one another."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "plt.plot(t_hm1[:,0],t_hm1[:,1])\n",
@@ -146,7 +140,6 @@
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
-    "collapsed": false,
     "scrolled": true
    },
    "outputs": [],
@@ -166,9 +159,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "import pandas\n",
@@ -184,7 +175,7 @@
     "pca_fit = pca.fit(X)\n",
     "Q = pca_fit.transform(X)\n",
     "\n",
-    "a = X.shape[0]/num_data_sets\n",
+    "a = int(X.shape[0]/num_data_sets)\n",
     "for i in range(X.shape[1]):\n",
     "    plt.plot(X[(i*a):((i+1)*a),3],\n",
     "             X[(i*a):((i+1)*a),4],\"o\")\n",
@@ -210,9 +201,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "pca_fit.explained_variance_ratio_"
@@ -240,9 +229,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "for i in range(Q.shape[1]):\n",
@@ -310,9 +297,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "f = open(\"pca_dataset.csv\")\n",
@@ -341,7 +326,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.5.2"
+   "version": "3.4.3"
   }
  },
  "nbformat": 4,