Given this table, find the best approximation of this function using least squares

Question

I am at the end of my ropes trying to get this question correct. I honestly have no idea what I'm doing wrong.

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"The table below lists the height h (in cm), the age a (in years), the gender g (0 = "Female", 1 = "Male"), and the weight w (in kg) of some college students.

$$\begin{array}{c|c|c|} \text{Height} & \text{Age} & \text{Gender} & \text{Weight}\\ \hline 155 & 21 & 0 & 47 \\ \hline 173 & 19 & 1 & 68 \\ \hline 175 & 20 & 1 & 70 \\ \hline 180 & 21 & 1 & 77 \\ \hline 160 & 22 & 0 & 52 \\ \hline \end{array}$$

We need to fit a linear function of the form: w = c₀ + c₁h + c₂a + c₃g.

Find the best approximation of this function, using least squares"

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We need to solve for the normal equation A^TAc = A^TB.

So I set up my two matrices as:

\begin{bmatrix} 1 & 155 & 21 & 0\\ 1 & 173 & 19 & 1\\ 1 & 175 & 20 & 1\\ 1 & 180 & 21 & 1\\ 1 & 160 & 22 & 0 \end{bmatrix}

and

\begin{bmatrix} 47 \\ 68 \\ 70 \\ 77 \\ 52 \end{bmatrix}

After plugging them into the formula and doing the calculations, I got the following values for c:

c₀ = -137.8333333331393

c₁ = 1.1666666666660603

c₂ = 0.16666666666606034

c₃ = 0.8333333333866904

Then it tells me to write my answer in this form:

w = w(h, a, g) = 

So I typed my answer as this:

-137.833 + 1.16667h + 0.166667a + 0.833333g

But it is completely wrong. Did I type it in the wrong format? Did I mess up my calculations? Or is it both cases?