def fit(self, data:[[float]], y:[float]) -> ([{}], [float], [float]):
logging.info("log: Linear Regression Model Fit Invoked.")
self.__validate(data, y)
self.__variables__ = len(data)
merge_data = [[None for x in range(len(y))] for x in range(len(data)+1)]
for i in range(len(merge_data)):
if i == 0:
merge_data[i] = y
else:
merge_data[i] = data[i-1]
self.__corr_mat__ = Statistics.correlation_matrix(merge_data)
self.__partial_mat__ = Statistics.partial_correlation_matrix(merge_data)
self.__stats__ = self.__stats(data, y)
m1, m2 = self.__regression_matrix(data, y)
m1i = Matrix.inverse(m1)
m1it = Matrix.transpose(m1i)
m2t = Matrix.transpose([m2])
params = Matrix.multiply(m1it, m2t)
params = Matrix.transpose(params)
params = params[0]
self.__params__ = params
self.__ycap__ = self.predicts(data)
self.__model_stats__ = self.__model_stats(y, self.__ycap__)
return (self.__stats__, self.__params__, self.__ycap__)
def test_var(self):
data_1 = [1, 2, 3, 4, 5, 6, 7, 8, 9]
actual = (statistics.variance(data_1),
math.sqrt(statistics.variance(data_1)))
expected = Statistics.variance(data_1)
self.assertEqual(expected, actual)
data_1_mean = Statistics.mean(data_1)
actual = Statistics.variance(data_1, data_1_mean)
self.assertEqual(expected, actual)
def pcf_data(ip, n):
op_list = []
for i in range(1, n+1):
lag_op = shift(ip, i)
op_tmp = list(Statistics.covariance(ip[i:], lag_op[i:]))
op_list.append([i, op_tmp[1]])
return op_list
def test_partial_correlation2(self):
y = [64, 71, 53, 67, 55, 58, 77, 57, 56, 51, 76, 68]
x1 = [57, 59, 49, 62, 51, 50, 55, 48, 52, 42, 61, 57]
x2 = [8, 10, 6, 11, 8, 7, 10, 9, 10, 6, 12, 9]
ry2_1 = Statistics.partial_correlation(y, x2, [x1])
ry2_1 = round(ry2_1, 3)
self.assertEqual(ry2_1, 0.335)
def test_partial_correlation1(self):
y = [64, 71, 53, 67, 55, 58, 77, 57, 56, 51, 76, 68]
x1 = [57, 59, 49, 62, 51, 50, 55, 48, 52, 42, 61, 57]
x2 = [8, 10, 6, 11, 8, 7, 10, 9, 10, 6, 12, 9]
ry1_2 = Statistics.partial_correlation(y, x1, [x2])
ry1_2 = round(ry1_2, 3)
self.assertEqual(ry1_2, 0.533)
def test_mean(self):
data_1 = [1, 2, 3, 4, 5, 6, 7, 8, 9]
actual = sum(data_1) / len(data_1)
expected = Statistics.mean(data_1)
self.assertEqual(expected, actual)
with self.assertRaises(TypeError):
Statistics.mean(["a", "b"])
data_2 = [
10.5, 2.1, 3.2, 0.4, 5.0000123, 6.78, 7.5234524, 8.2654672,
9.1645164
]
actual = sum(data_2) / len(data_2)
expected = Statistics.mean(data_2)
self.assertEqual(expected, actual)
def __stats(self, data: [[float]], y: [float]) -> []:
stats = [{} for i in range(len(data) + 1)]
y_stats = Statistics.describe(y)
(y_variance, y_std) = Statistics.variance(y, y_stats["mean"])
y_stats["covariance"] = y_variance
y_stats["r"] = 1.0
y_stats["pr"] = 1.0
stats[0] = y_stats
for i in range(len(data)):
s = Statistics.describe(data[i])
(covariance, r) = Statistics.covariance(data[i], y, s["mean"],
y_stats["mean"])
s["covariance"] = covariance
s["r"] = r
s["pr"] = self.__partial_mat__[0][i + 1]
stats[i + 1] = s
return stats
def test_partial_correlation_4data(self):
x1 = [75, 83, 85, 85, 92, 97, 99]
x2 = [1.85, 1.25, 1.5, 1.75, 1.15, 1.75, 1.6]
x3 = [16, 20, 25, 27, 32, 48, 48]
x4 = [14, 21, 29, 16, 21, 47, 47]
r12_34 = Statistics.partial_correlation(x1, x2, [x3, x4])
r12_34 = round(r12_34, 3)
self.assertEqual(r12_34, -0.961)
def test_describe(self):
data = [1, 2, 3, 4, 5, 6, 7, 8, 9]
stats = Statistics.describe(data)
self.assertEqual(stats["count"], 9)
self.assertEqual(stats["mean"], 5.0)
self.assertEqual(stats["variance"], 7.5)
self.assertEqual(stats["std"], 2.7386127875258306)
self.assertEqual(stats["min"], 1)
self.assertEqual(stats["max"], 9)
def test_partial_correlation_coefficient_greater_than_r(self):
#https://stackoverflow.com/questions/51236206/partial-correlation-values-are-larger-than-normal-correlation-in-r
hl = [7, 15, 19, 15, 21, 22, 57, 15, 20, 18]
disp = [
0.000, 0.964, 0.000, 0.000, 0.921, 0.000, 0.000, 1.006, 0.000,
1.011
]
deg = [9, 2, 3, 4, 1, 3, 1, 3, 6, 1]
BC = [
1.78e-02, 1.05e-06, 1.37e-05, 7.18e-03, 0.00e+00, 0.00e+00,
0.00e+00, 4.48e-03, 2.10e-06, 0.00e+00
]
var, r = Statistics.covariance(hl, disp)
r = round(r, 5)
self.assertEqual(r, -0.23787)
pr = Statistics.partial_correlation(hl, disp, [deg, BC])
pr = round(pr, 5)
self.assertEqual(pr, -0.67209)
mat = Statistics.partial_correlation_matrix([hl, disp, deg, BC])
mat_pr = round(mat[0][1], 5)
self.assertEqual(mat_pr, -0.67209)
def test_correlation_matrix_4data(self):
x1 = [75, 83, 85, 85, 92, 97, 99]
x2 = [1.85, 1.25, 1.5, 1.75, 1.15, 1.75, 1.6]
x3 = [16, 20, 25, 27, 32, 48, 48]
x4 = [14, 21, 29, 16, 21, 47, 47]
mat = Statistics.correlation_matrix([x1, x2, x3, x4])
actual = [[
1.0, -0.15534261150561485, 0.9627972334240521, 0.8520652907262152
], [
-0.15534261150561485, 1.0, 0.10551846545168846, 0.13506331370887886
], [0.9627972334240521, 0.10551846545168846, 1.0, 0.9088795720039011],
[
0.8520652907262152, 0.13506331370887886,
0.9088795720039011, 1.0
]]
self.assertEqual(mat, actual)
def test_partial_correlation_matrix_4data(self):
x1 = [75, 83, 85, 85, 92, 97, 99]
x2 = [1.85, 1.25, 1.5, 1.75, 1.15, 1.75, 1.6]
x3 = [16, 20, 25, 27, 32, 48, 48]
x4 = [14, 21, 29, 16, 21, 47, 47]
mat = Statistics.partial_correlation_matrix([x1, x2, x3, x4])
actual = [[
1.0, -0.9613273119340023, 0.9866069072448754, -0.3903841491779091
], [-0.9613273119340022, 1.0, 0.9465782218637125, -0.3513457030175387],
[
0.9866069072448754, 0.9465782218637125, 1.0,
0.5215083165976273
],
[
-0.3903841491779091, -0.35134570301753876,
0.5215083165976273, 1.0
]]
self.assertEqual(mat, actual)
def test_covariance(self):
data_x_1 = [1, 2, 3, 4, 5, 6, 7, 8, 9]
data_y_1 = [1, 2, 3, 4, 5, 6, 7, 8, 9]
actual = (7.5, 1)
expected = Statistics.covariance(data_x_1, data_y_1)
self.assertEqual(expected, actual)
with self.assertRaises(ValueError):
Statistics.covariance([1, 2, 3], [1, 2])
data_x_1_mean = Statistics.mean(data_x_1)
data_y_1_mean = Statistics.mean(data_y_1)
expected = Statistics.covariance(data_x_1, data_y_1, data_x_1_mean,
data_y_1_mean)
self.assertEqual(expected, actual)
def __model_stats(self, y:[float], ycap:[float]) -> {}:
error = [0.0 for x in range(len(y))]
for i in range(len(y)):
error[i] = y[i] - ycap[i]
s = Statistics.describe(error)
return s
def test_yule_walker2(self):
r12_3 = Statistics.yule_walker_eq(0.774, 0.819, 0.802)
self.assertEqual(r12_3, 0.3418386394082465)
def test_yule_walker1(self):
r12_3 = Statistics.yule_walker_eq(0.819, 0.774, 0.802)
self.assertEqual(r12_3, 0.5241753109234627)
def test_correlation_coefficient(self):
data_x_1 = [1, 2, 3, 4, 5, 6, 7, 8, 9]
data_y_1 = [1, 2, 3, 4, 5, 6, 7, 8, 9]
actual = 1
expected = Statistics.correlation_coefficient(7.5, 7.5, 7.5)
self.assertEqual(expected, actual)
def test_partial_correlation_none_data(self):
with self.assertRaises(ValueError):
Statistics.partial_correlation(None, [1], [[2]])
with self.assertRaises(ValueError):
Statistics.partial_correlation([1], None, [[2]])
with self.assertRaises(ValueError):
Statistics.partial_correlation([1], [1], None)
with self.assertRaises(ValueError):
Statistics.partial_correlation([], [1], [[1]])
with self.assertRaises(ValueError):
Statistics.partial_correlation([1], [], [[1]])
with self.assertRaises(ValueError):
Statistics.partial_correlation([1], [1], [[]])
with self.assertRaises(ValueError):
Statistics.partial_correlation([1], [1], [[1, 2]])
with self.assertRaises(ValueError):
Statistics.partial_correlation([1], [1, 2], [[1, 2]])
def test_yule_walker_none_data(self):
with self.assertRaises(ValueError):
Statistics.yule_walker_eq(None, 0.774, 0.802)
with self.assertRaises(ValueError):
Statistics.yule_walker_eq(1, None, 0.802)
with self.assertRaises(ValueError):
Statistics.yule_walker_eq(1, 0.774, None)
with self.assertRaises(ValueError):
Statistics.yule_walker_eq(1.2, 0.774, 0.802)
with self.assertRaises(ValueError):
Statistics.yule_walker_eq(1, 1.2, 0.802)
with self.assertRaises(ValueError):
Statistics.yule_walker_eq(1, 0.774, -1.2)
def test_none_data(self):
with self.assertRaises(ValueError):
Statistics.mean(None)
with self.assertRaises(ValueError):
Statistics.mean([])
with self.assertRaises(ValueError):
Statistics.variance(None)
with self.assertRaises(ValueError):
Statistics.variance([])
with self.assertRaises(ValueError):
Statistics.covariance(None, [1])
with self.assertRaises(ValueError):
Statistics.covariance([], [1])
with self.assertRaises(ValueError):
Statistics.covariance([1], None)
with self.assertRaises(ValueError):
Statistics.covariance([1], [])
with self.assertRaises(ValueError):
Statistics.covariance([1], [1, 2])
