Question

[Q#2] (8pts) For the following data set, compute the equation of the least-squares regression line and correlation coefficient. 13 20 25 27 8 8 15 7 6 4 6 5

Answer 1

Soluhon: We have dataset as given Sr. No. di Y; 8 - 8 X; Y; 64 78 2 13 6 y? 64 36 49 16 3 15 x, 64 169 225 400 625 729 105 4 7 4 6 20 80 25 36 150 S 6 27 S 25 135 Total 108 36 2212 226 612 line and Question Compute the correlahon coefficienti equation of regression i Mean of n Ο ΣΧ nic = 18 11 1 * 108 6 E(X)=Mean (x) ii) Mean of yin n 1 gyi n 1) * 36 Ğ E(Y) : mém (y) = iii) E Cx²0 : E(X²) Ο Σας 1 * 2212 = 368.6667 - ) = 5 iv) E (72) 37.6667 I'My y ? c 1 * 226 6 Ecy?): v) E (XY) !- E(XY)= o Ž ca; *y;) S 6*612 : 102

Now, The least squove regoession line is given by Y; = a +bX; a: Ely) - b E(X) E (xy) - E(X) + E CY) E (x2) - [£(x]? where b = as E(Y)- b E (x) from i) and °) a 6 - b* 18 la= 6-186] O and ba E(XY) - ECx) · ECY) E(x²) (EC)]? 102 - 1876 368,6667 - (1832 ba ba 44.6667 ba - 0.13 63 63 b -0.1364 rounded to 4 decimal 2 Put this b in 6 , we get a: 6 - 18 *(-0.1364) a : 6+ 2.4545 a = 8.4545 ( from * ② and the the least square regression Syon line is Y = 8.4545 - 0.1364 Xi

And correlation coefficient (r) fermula is ECXY) - E (X). ECY) F(x3) - LEW)]2 * VE(Y3- (E(X)) 72 102 - 18*6 V 368.6667-182 * V 37.6667-62. -6 = V44.6667 V 1.6667 Vab = Va *vb V 44.6667 * 1.6667 -6 8.6281194 r=-0.6954 S i) The least square regression data set is Result! from 6 and 6 ion line for given y = 8.4545 -0.1364 % ii) The comelahion coefficient berween and y 72 -0.69 54 That is there is negative Corme lahon betwee x and y