def solve_simple_regression(x,y):
""" solve simple regression coefficients
returns w_0 (slope) and w_1 (intercept)
>>> solve_simple_regression(range(9),[19, 20, 20.5, 21.5, 22, 23, 23, 25.5, 24])
(0.7166666666666667, 19.18888888888889)
"""
n = float(len(x))
slope = (dot(y,x) - ((sum(y)*sum(x))/n))/(dot(x,x)-((sum(x)*sum(x))/n))
intercept = sum(y)/n - slope*sum(x)/n
return slope, intercept
def solve_simple_regression(x, y):
""" solve simple regression coefficients
returns w_0 (slope) and w_1 (intercept)
>>> solve_simple_regression(range(9),[19, 20, 20.5, 21.5, 22, 23, 23, 25.5, 24])
(0.7166666666666667, 19.18888888888889)
"""
n = float(len(x))
slope = (dot(y, x) - ((sum(y) * sum(x)) / n)) / (dot(x, x) -
((sum(x) * sum(x)) / n))
intercept = sum(y) / n - slope * sum(x) / n
return slope, intercept
def residual_sum_of_squares(input_feature, output, slope, intercept):
""" simple regression model based on input coefficients
input: input_feature (x vector), output (y vector), slope(w_0), intercept (w_1)
output: rss
"""
predictions = get_regression_predictions(input_feature, slope, intercept)
residuals = output - predictions
rss = dot(residuals, residuals)
return (rss)
def residual_sum_of_squares(input_feature, output, slope, intercept):
""" simple regression model based on input coefficients
input: input_feature (x vector), output (y vector), slope(w_0), intercept (w_1)
output: rss
"""
predictions = get_regression_predictions(input_feature, slope, intercept)
residuals = output - predictions
rss = dot(residuals, residuals)
return(rss)
def covariance(x,y):
""" measure dispersion in another way
>>> covariance([1,2,3,4,5,6],[1,2,3,4,5,7])
4.0
"""
return dot(from_mean(x), from_mean(y)) / (len(x) - 1)
