TheAlgorithms/Python · error · ValueError

Data must have dimensions N x 1

Error message

Data must have dimensions N x 1

What it means

Thrown by PolynomialRegression._design_matrix when the input data is not a 1-D array of shape (N,). The design matrix is built with np.vander over a flat vector of predictor values; any 2-D input like (N, 2) has no defined polynomial expansion here and is rejected by unpacking data.shape and checking for leftover dimensions.

Source

Thrown at machine_learning/polynomial_regression.py:98

        array([[1, 0],
               [1, 1],
               [1, 2]])
        >>> PolynomialRegression._design_matrix(x, degree=2)
        array([[1, 0, 0],
               [1, 1, 1],
               [1, 2, 4]])
        >>> PolynomialRegression._design_matrix(x, degree=3)
        array([[1, 0, 0, 0],
               [1, 1, 1, 1],
               [1, 2, 4, 8]])
        >>> PolynomialRegression._design_matrix(np.array([[0, 0], [0 , 0]]), degree=3)
        Traceback (most recent call last):
        ...
        ValueError: Data must have dimensions N x 1
        """
        _rows, *remaining = data.shape
        if remaining:
            raise ValueError("Data must have dimensions N x 1")

        return np.vander(data, N=degree + 1, increasing=True)

    def fit(self, x_train: np.ndarray, y_train: np.ndarray) -> None:
        """
        Computes the polynomial regression model parameters using ordinary least squares
        (OLS) estimation:

        β = (XᵀX)⁻¹Xᵀy = X⁺y

        where X⁺ denotes the Moore-Penrose pseudoinverse of the design matrix X. This
        function computes X⁺ using singular value decomposition (SVD).

        References:
            - https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse
            - https://en.wikipedia.org/wiki/Singular_value_decomposition
            - https://en.wikipedia.org/wiki/Multicollinearity

View on GitHub (pinned to f5988cc097)

Solutions

1. Flatten the input: data = np.asarray(data).ravel() before calling fit/predict.
2. For multivariate inputs, use a multivariate regression method instead of this class.
3. Select DataFrame columns with a single bracket: df['x'] not df[['x']].

Example fix

# before
x = df[['x']].to_numpy()          # shape (N, 1)
model.fit(x, y)

# after
x = df['x'].to_numpy()            # shape (N,)
model.fit(x, y)

x = np.asarray(x).ravel()
assert x.ndim == 1
model.fit(x, y)

def is_1d_array(data: np.ndarray) -> bool:
    return isinstance(data, np.ndarray) and data.ndim == 1

When it happens

Trigger: Passing np.array([[0, 0], [0, 0]]) or any (N, M) matrix with M > 1 to _design_matrix, fit, or predict; passing a column vector of shape (N, 1) also raises because a second dimension remains.

Common situations: Multivariate feature matrices fed to a univariate fitter; sklearn-style column vectors (N, 1) not flattened; DataFrame column selected with double brackets producing 2-D.

Related errors

• Input data set must be one-dimensional
• Data set labels must be one-dimensional
• Shape of y_true and y_pred must be the same.
• Expected the same number of rows for A and B. Instead found
• Expected the same number of columns for B and C. Instead fou

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/e223741b593735e5. Report an issue: GitHub.