Error cost function shape

In the following slide we learn that squared error cost is not always convex:

I don’t understand the answer in this thread:

So I have a question. For linear regression squared error cost function is always convex. Can we say the same for the polynomial regression we saw in week 1?

And we can say that the cost function that we learn in week 2:

is convex also when we choose non-linear decision boundaries?

Thank you

My reply applied to linear regression - not logistic.

The logistic cost function is also known to be convex, because it doesn’t use the squared error.

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Yes, we can say that. The cost is the sum of the squared errors - it does not matter how the features are created.

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