"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"The quadratic equation is y = -20.967 + 2.996x - 0.046x^2\n"
]
}
],
"source": [
"pr.plot_polynomial(xs, ys, xhat, degree=2, x_min=5, x_max=60)\n",
"\n",
"print()\n",
"print(f'The quadratic equation is y = {xhat[0]:.3f}', end='')\n",
"if xhat[1] >= 0: \n",
" print(f' + {xhat[1]:.3f}x', end ='')\n",
"else:\n",
" print(f' - {-xhat[1]:.3f}x', end ='')\n",
"\n",
"if xhat[2] >= 0: \n",
" print(f' + {xhat[2]:.3f}x^2', end ='')\n",
"else:\n",
" print(f' - {-xhat[2]:.3f}x^2')\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"#### PROBLEM 2. If you have n points and you generate a least-squares polynomial of degree n-1, you've calculated the interpolation line that runs through all n points. This is also known as polynomial curve fitting.\n",
"\n",
"#### Calculate and plot the interpolation line for these points: (-2, 3), (-1, 5), (0, 1), (1, 4), and (2, 10).\n",
"\n",
"#### SOLUTION:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"xs = [-2, -1, 0, 1, 2]\n",
"ys = [3, 5, 1, 4, 10]"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1, -2, 4, -8, 16],\n",
" [ 1, -1, 1, -1, 1],\n",
" [ 1, 0, 0, 0, 0],\n",
" [ 1, 1, 1, 1, 1],\n",
" [ 1, 2, 4, 8, 16]])"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A = np.array([[xs[i]**j for j in range(len(xs))] for i in range(len(xs))]) \n",
"A"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 3, 5, 1, 4, 10])"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"b = np.array(ys)\n",
"b"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1. , -1.25 , 4.20833333, 0.75 , -0.70833333])"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a = solve(A, b)\n",
"a"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pr.plot_polynomial(xs, ys, a, degree=len(xs)-1, x_min=-2.3, x_max=3, y_axis_pos=0, size=(6, 6))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"#### PROBLEM 3.a. Amalgamated Widgets, Inc. ranks its employees by productivity: 1 (lowest), 2, 3, and 4 (highest). The following table shows for each rank, at the start of a new training program, the percentage of employees, the percentage productivity loss per employee, and the total percentage productivity loss.\n",
"\n",
"
\n",
"
Rank
Employees
x
Productivity loss
=
Total loss
\n",
"
1
30%
40%
12.00%
\n",
"
2
35%
25%
8.75%
\n",
"
3
25%
15%
3.75%
\n",
"
4
10%
5%
0.50%
\n",
"
Overall total
25.00%
\n",
"
\n",
"\n",
"#### The training supervisor provided the following table that predicts what percentage of employees will move from one rank to another or stay in the same rank after each hourly training session, as determined by a test given at the end of the hour:\n",
"\n",
"