Python Multiple Simple Linear Regression

Question

Note this is not a question about multiple regression, it is a question about doing simple (single-variable) regression multiple times in Python/NumPy (2.7).

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Answer 1

Single variable linear regression is simple enough to vectorize it manually:

def multiple_linregress(x, y):
    x_mean = np.mean(x, axis=1, keepdims=True)
    x_norm = x - x_mean
    y_mean = np.mean(y, axis=1, keepdims=True)
    y_norm = y - y_mean

    slope = (np.einsum('ij,ij->i', x_norm, y_norm) /
             np.einsum('ij,ij->i', x_norm, x_norm))
    intercept = y_mean[:, 0] - slope * x_mean[:, 0]

    return np.column_stack((slope, intercept))

With some made up data:

m = 1000
n = 1000
x = np.random.rand(m, n)
y = np.random.rand(m, n)

it outperforms your looping options by a fair margin:

%timeit multiple_linregress(x, y)
100 loops, best of 3: 14.1 ms per loop