Question

(1 point) The table below lists the height h (in cm), the age a (in years), the gender g (1="Male", O="Female"), and the weight w (in kg) of some college students. 0 Height Age Gender Weight 162 21 61 165 19 64 171 19 156 23 0 184 221 95 80 55 We wish to fit a linear function of the form f(t) = co+ch + c2a + c39 to these data. Find the best approximation of this form, using least squares.

Answer 1

f(t) = Co+C, h + Gao +(39 observation I: " 2: " 3: 1 4: " 5: Co + 162c, +21 C2 to.G - 61 Co + 1656, +1952 +o.cz - 64 Co+1716, +19€ + 1.63 = 80 Co + 156 C, +232 + 0.cz = 55 Co +184 S; + 2262 +1.C3 =95 In matrix form, 1 162 1 165 I 171 1156 I 184 21 19 19 -o-oo ů J W = b ů o N m م ت 3 A b = (ATA)! A?. b ; where : A = pseudo-inverse of A. ال

Using WolframAlpha to calculate (A^T) * A:

transpose({{1,162,21,0}, {1,165,19,0}, {1,171,19,1}, {1,156,23,0}, {1,184,22,1}}) * {{1,162,21,0}, {1,165,19, B Sja Extended Keyboard Upload Examples 4 Random Input: (1 162 21 0 (1 162 21 0 1 165 19 0 1 165 19 1 171 19 1 . 1 171 19 1 1 156 23 0 1 156 23 0 (1 184 22 1) (1 184 22 1 m' gives the transpose of m Result: ( 5 838 104 2 838 140 902 17422 355 104 17422 2176 41 2 355 412)

Ý J W 5 838 106 2 1838 140902 17422 355 104 17422 2176 41 12 355 4 21

Using WolframAlpha to calculate ((A^T) * A)^-1 * A^T * b:

inverse({{5,838,104,2}, {838,140902,17422,355}, {104,17422,2176,41}, {2,355,41,2}}) * transpose({{1,11 6 Sia Extended Keyboard Upload Examples Random Input: (5 838 104 2 838 140 902 17422 355 104 17422 2176 41 12 355 412 -1 (1 162 21 0 | 1 165 19 0 . 1 171 19 1. 1 156 23 0 (1 184 22 1) m' gives the transpose of m Exact result: 1 1579 1-192477 1737 360 14942

- 192477 S ů j w 1737 > answeg. 1579 360 14942 M