def get_b0b1(self, x, y):
"""
In simple linear regression, b1 is the slope of the regression line.
b0 is the intercept of the regression line with the y-axis.
Equation for the simple regression line : y-hat = b0 + b1*x
:param x: a list of x values for a series of points
:param y: a list of y values for a series of points
:return: b0, b1
"""
x_bar = mean(x)
y_bar = mean(y)
x_minus_xbar = [i - x_bar for i in x]
y_minus_ybar = [j - y_bar for j in y]
b1_column_denom = [i * j for i, j in zip(x_minus_xbar, y_minus_ybar)]
b1_column_num = [i**2 for i in x_minus_xbar]
numerator = sum(b1_column_denom)
denominator = sum(b1_column_num)
b1 = numerator / denominator
b0 = y_bar - (b1 * x_bar)
return b0, b1
def get_b0b1(self, x, y):
"""
In simple linear regression, b1 is the slope of the regression line.
b0 is the intercept of the regression line with the y-axis.
Equation for the simple regression line : y-hat = b0 + b1*x
:param x: a list of x values for a series of points
:param y: a list of y values for a series of points
:return: b0, b1
"""
x_bar = mean(x)
y_bar = mean(y)
x_minus_xbar = [i - x_bar for i in x]
y_minus_ybar = [j - y_bar for j in y]
b1_column_denom = [i*j for i, j in zip(x_minus_xbar, y_minus_ybar)]
b1_column_num = [i**2 for i in x_minus_xbar]
numerator = sum(b1_column_denom)
denominator = sum(b1_column_num)
b1 = numerator / denominator
b0 = y_bar - (b1 * x_bar)
return b0, b1
def r_squared(self, x, y):
"""
R-squared is a statistical measure of how close the data is to the
fitted regression line.
It is also known as the coefficient of determination.
The higher the value of R squared, the better the model fits your data.
R is always between 0 and 1.
:param x: a list of x values for a series of points
:param y: a list of y values for a series of points
:return: r_squared
"""
y_bar = mean(y)
y_minus_ybar = [j - y_bar for j in y]
y_minus_ybar_squared = [j**2 for j in y_minus_ybar]
b0, b1 = self.get_b0b1(x, y)
y_hat = [b0 + b1 * i for i in x]
yhat_minus_ybar = [yh - y_bar for yh in y_hat]
yhat_minus_ybar_squared = [h**2 for h in yhat_minus_ybar]
r_squared = sum(yhat_minus_ybar_squared) / sum(y_minus_ybar_squared)
return r_squared
def r_squared(self, x, y):
"""
R-squared is a statistical measure of how close the data is to the
fitted regression line.
It is also known as the coefficient of determination.
The higher the value of R squared, the better the model fits your data.
R is always between 0 and 1.
:param x: a list of x values for a series of points
:param y: a list of y values for a series of points
:return: r_squared
"""
y_bar = mean(y)
y_minus_ybar = [j - y_bar for j in y]
y_minus_ybar_squared = [j ** 2 for j in y_minus_ybar]
b0, b1 = self.get_b0b1(x, y)
y_hat = [b0 + b1 * i for i in x]
yhat_minus_ybar = [yh - y_bar for yh in y_hat]
yhat_minus_ybar_squared = [h ** 2 for h in yhat_minus_ybar]
r_squared = sum(yhat_minus_ybar_squared) / sum(y_minus_ybar_squared)
return r_squared
def scale(data_matrix):
"""returns the mean and standard deviation of each column"""
num_rows, num_cols = shape(data_matrix)
means = [mean(get_column(data_matrix,j)) for j in range(num_cols)]
stdevs = [standard_deviation(get_column(data_matrix, j))
for j in range(num_cols)]
return means, stdevs
def scale(data_matrix):
"""returns the mean and standard deviation of each column"""
num_rows, num_cols = shape(data_matrix)
means = [mean(get_column(data_matrix, j)) for j in range(num_cols)]
stdevs = [
standard_deviation(get_column(data_matrix, j)) for j in range(num_cols)
]
return means, stdevs
def de_mean(x):
"""translate x by subtracting its mean (so the result has mean 0)"""
x_bar = mean(x)
return [x_i - x_bar for x_i in x]
