def REGRESSION(x_list, y_list):
"""
Regression
Returns: dict of lists of floats = jhta.REGRESSION(x_list, y_list)
Source: https://www.wallstreetmojo.com/regression-formula/
"""
xy_list = []
x2_list = []
for i in range(len(x_list)):
x = x_list[i]
y = y_list[i]
xy = x * y
x2 = x * x
xy_list.append(xy)
x2_list.append(x2)
# set n:
n = len(x_list)
# sum it:
x_sum = jhta.SUM({'x_list': x_list}, n, 'x_list')[-1]
y_sum = jhta.SUM({'y_list': y_list}, n, 'y_list')[-1]
xy_sum = jhta.SUM({'xy_list': xy_list}, n, 'xy_list')[-1]
x2_sum = jhta.SUM({'x2_list': x2_list}, n, 'x2_list')[-1]
# calculate intercept:
a = ((y_sum * x2_sum) - (x_sum * xy_sum)) / (n * x2_sum - x_sum**2)
# calculate slope:
b = ((n * xy_sum) - (x_sum * y_sum)) / (n * x2_sum - x_sum**2)
estimate_list = []
err_list = []
err2_list = []
for i in range(len(x_list)):
x = x_list[i]
y = y_list[i]
# calculate estimate:
yes = a + b * x
estimate_list.append(yes)
# calculate error:
err = y - yes
err_list.append(err)
# calculate square error:
err2 = err**2
err2_list.append(err2)
return {'estimate': estimate_list, 'err': err_list, 'err2': err2_list}
def LSR(df, price='Close', predictions_int=0):
"""
Least Squares Regression
"""
x_list = []
y_list = []
x2_list = []
xy_list = []
i = 0
while i < len(df[price]):
# For each (x,y) calculate x2 and xy:
x = i
y = df[price][i]
x2 = x * x
xy = x * y
x_list.append(x)
y_list.append(y)
x2_list.append(x2)
xy_list.append(xy)
i += 1
# Sum all x, y, x2 and xy, which gives us Σx, Σy, Σx2 and Σxy:
x_sum = jhta.SUM({'x_list': x_list}, len(x_list), 'x_list')[-1]
y_sum = jhta.SUM({'y_list': y_list}, len(y_list), 'y_list')[-1]
x2_sum = jhta.SUM({'x2_list': x2_list}, len(x2_list), 'x2_list')[-1]
xy_sum = jhta.SUM({'xy_list': xy_list}, len(xy_list), 'xy_list')[-1]
# set n:
n = len(df[price])
# Calculate Slope:
m = (n * xy_sum - x_sum * y_sum) / (n * x2_sum - x_sum * x_sum)
# Calculate Intercept:
b = (y_sum - m * x_sum) / n
lsr_list = []
i = 0
while i < len(df[price]) + predictions_int:
# Assemble the equation of a line:
lsr = m * i + b
lsr_list.append(lsr)
i += 1
return lsr_list
def LSR(df, price='Close', predictions_int=0):
"""
Least Squares Regression
Returns: list of floats = jhta.LSR(df, price='Close', predictions_int=0)
Source: https://www.mathsisfun.com/data/least-squares-regression.html
"""
x_list = []
y_list = []
x2_list = []
xy_list = []
for i in range(len(df[price]) - predictions_int):
# For each (x,y) calculate x2 and xy:
x = i
y = df[price][i]
x2 = x * x
xy = x * y
x_list.append(x)
y_list.append(y)
x2_list.append(x2)
xy_list.append(xy)
# Sum all x, y, x2 and xy, which gives us Σx, Σy, Σx2 and Σxy:
x_sum = jhta.SUM({'x_list': x_list}, len(x_list), 'x_list')[-1]
y_sum = jhta.SUM({'y_list': y_list}, len(y_list), 'y_list')[-1]
x2_sum = jhta.SUM({'x2_list': x2_list}, len(x2_list), 'x2_list')[-1]
xy_sum = jhta.SUM({'xy_list': xy_list}, len(xy_list), 'xy_list')[-1]
# set n:
n = len(df[price]) - predictions_int
# Calculate Slope:
m = (n * xy_sum - x_sum * y_sum) / (n * x2_sum - x_sum * x_sum)
# Calculate Intercept:
b = (y_sum - m * x_sum) / n
# Assemble the equation of a line:
return [m * i + b for i in range(len(df[price]))]
def INFO(df, price='Close'):
"""
Print df Information
"""
print('{:_<28}:{:_>22}'.format('DF PRICE COLUMN', price))
print('{:_<28}:{:_>22d}'.format('LEN', len(df[price])))
print('{:_<28}:{:_>28.5f}'.format('MIN',
jhta.MIN(df, len(df[price]), price)[-1]))
print('{:_<28}:{:_>28.5f}'.format('MAX',
jhta.MAX(df, len(df[price]), price)[-1]))
print('{:_<28}:{:_>28.5f}'.format('SUM',
jhta.SUM(df, len(df[price]), price)[-1]))
print('{:_<28}:{:_>28.5f}'.format('MEAN',
jhta.MEAN(df, len(df[price]),
price)[-1]))
# print ('{:_<28}:{:_>28.5f}'.format('HARMONIC_MEAN', jhta.HARMONIC_MEAN(df, len(df[price]), price)[-1]))
print('{:_<28}:{:_>28.5f}'.format(
'MEDIAN',
jhta.MEDIAN(df, len(df[price]), price)[-1]))
print('{:_<28}:{:_>28.5f}'.format(
'MEDIAN_LOW',
jhta.MEDIAN_LOW(df, len(df[price]), price)[-1]))
print('{:_<28}:{:_>28.5f}'.format(
'MEDIAN_HIGH',
jhta.MEDIAN_HIGH(df, len(df[price]), price)[-1]))
print('{:_<28}:{:_>28.5f}'.format(
'MEDIAN_GROUPED',
jhta.MEDIAN_GROUPED(df, len(df[price]), price)[-1]))
# print ('{:_<28}:{:_>28.5f}'.format('MODE', jhta.MODE(df, len(df[price]), price)[-1]))
print('{:_<28}:{:_>28.5f}'.format(
'PSTDEV',
jhta.PSTDEV(df, len(df[price]), price)[-1]))
print('{:_<28}:{:_>28.5f}'.format(
'PVARIANCE',
jhta.PVARIANCE(df, len(df[price]), price)[-1]))
print('{:_<28}:{:_>28.5f}'.format(
'STDEV',
jhta.STDEV(df, len(df[price]), price)[-1]))
print('{:_<28}:{:_>28.5f}'.format(
'VARIANCE',
jhta.VARIANCE(df, len(df[price]), price)[-1]))