Why Am I Getting a 'operands could not be broadcast together' Error in NumPy?

Understanding the Error: 'operands could not be broadcast together' in NumPy

When working with NumPy arrays, it's crucial to pay attention to array shapes to avoid broadcasting errors. In the given scenario, you encountered the error "ValueError: operands could not be broadcast together with shapes."

This error occurs because NumPy's operators, such as *, perform element-wise operations by default. However, if the arrays have different shapes, NumPy attempts to broadcast them, which can lead to compatibility issues.

Broadcasting Rules and Compatibility

Broadcasting involves expanding dimensions of one or both arrays to make them compatible for element-wise operations. Dimensions of size 1 or missing dimensions can be broadcast.

In your case, X has a shape of (97, 2) and y has a shape of (2, 1). Broadcasting the dimensions would result in:

  97    2
   2    1

As you can see, the first dimension (97 and 2) conflicts. According to broadcasting rules, conflicting dimensions must be the same or one of them should be 1.

Resolving the Broadcast Error

To resolve this issue, you need to ensure that the dimensions of the arrays are compatible. In your case, you can use NumPy's dot product, which performs matrix multiplication:

X.dot(y)

Matrix multiplication follows different compatibility rules, ensuring that the number of columns in the first array matches the number of rows in the second array. Since X has 2 columns and y has 2 rows, matrix multiplication is valid, resulting in a vector with a shape of (97, 1).

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