Question

We have a dataset with n = 10 pairs of observations (Li, Yi), and n X; = 683, Yi = 813, i=1 i=1 2* = 47, 405, XiYi = 56,089, Cy? = 66, 731. i=1 i=1 i=1 What is the coefficient of correlation for this data? We have a dataset with n = 10 pairs of observations (li, Yi), and di = 683, Yi = 813, n x* = 47,405, x:yi = 56,089, y = 66, 731. i=1 i=1 i=1 What is an approximate 95% confidence interval for the intercept of the line of best fit?

Answer 1

Ani fir na lo pure og observation (xi, Y.) X; = 683. [ Y; - 013, x;2=47405, SX; 9; = 56089 4,2=66,731

8= The correlation coefficient, say r blw (Gylie n Exiy; - (EX;)Eyi) Vin E 12-158/12 ] [n {y; ?-1843)2] 561) 10 X 56089 - 683X 813 17561X 6347 (10x47405-1603)2] [10X66731- () 3)2] 5611 ♡ 0.0103 6924.1823 Il.

bi The estimate of slope say bi of the line of best fit in SX4,- (5X; 159; n 37; 2- (EX,12 10 X 50001 - 603x813 560290-555279 10x47405- (68372 474050-466489 bi 5611 Pube 0.7421 7561 The gst approximate confidence interval for slope is wat 1b, + +(1-2) V20-235** ssies (N-2)S3X Sword Dog where stres - Syy- biscy bowlad ynx) Roy and Syy= 2y;2_n 92 = 66731- 10 X (2013)? 2 634. Sxy = {1xi-Er) (Yr J) = {x,y; - n5c ý 5608910X683 x 013 561.1 and Swix = E(Xi-8125 sxi? n152 = 47405-10X(683)? = 47405- 46648.9= 756.1 and so the approximate 95./..C.I. for slope is 10 10 0.74 21. I 2.306 634.1-0.7421X 561.1 &'x 756.1 (Rincias th-2,415 for n-2=8, 2.3060 q=0.05 (0:7421 +0:4315), = (0.30 46; 1.1796)