Question

We have a dataset with n = 10 pairs of observations (Li, Yi), and n τη α, = 683, 9 = 813, 1=1 Σ Σ? = 47, 405, Στ.μ. = 56, 089, Συ? = 66, 731. ΤΟ =1 1=1 What is the line of best fit for this data?

Answer 1

x = { x 683 n=10 47605-68.39 x 10 ssy = 66731 -10 (813) 2 Ssxy = {(xy-nă ý = 56089-10(68.3) ( 8 1-3 Given 68.3 y = {yi 813 81.3 Ssx = {x, ² nx2 = Ss x = 756.1 Ssy= {4; 2- nğ2 = 634.1 =561.1 B, & SS ry solit -0.742098 SSX 75611 SSTotal = ssy = 634.1 SSReg = P, Ssxy = = 561.1 X0.742098 -416.390967 SSE = SS Total - ssreg= 63411-416.390967 = 217. 7090 33 SECB, ) = SSE (0-2) 27.213629) 75611 SE (B) =00189 7 15848 Ssxy = 0.035992103 ssy

mean ů 11. = 75.1407 llylko tit 95% confidence interval for the response ad H=60 frediction interval is Confidence 1 + (xorde ta/ 1-2 = 2.306 T s sx 756.) (75.1407 - 2:306x5.21666839 +(60-68.3² (15.14071 12.0296373 Jogail229 (75.140712.0296373x 0.437163917) (75.1407 + 5.25892336) (69.88177 80.3996234 ) (69.8818, 80.3996) for mean is 954 2 confidence interval response at Xo =60

gg.s. confidence interval for intercept. 0.01 020 25 0.005 2/2 10-2 = 3,3.55 Se (Bo) = MSE [5+2 {(x-7) 2 27,21 36291 [to +(68.332 170.620564 Se (B): 13.062 1807 756. I confidence interval Po t to/₂n-2 Se (B) 30.6147 - 3.355 x 13.0621807 30.6147 # 43.8236162) -13,2089162,74.4383 162 => (-13:2089,74.4383)

(0.74 2098 I 3355 Xo. 189715848 . (0.742098 + 0.63649667) x = 1% = 0.01 a/2=0.oos taizin-z = 3.355 Confidence interval Se CÊ ß t tx/2 ☺ 1+ 37859 gg.). CI is (0, 1056, 1.3786)