Question

ما کر 10. A group of 13 children and adolescents (considered healthy) participated in a psychological study designed to analyze the relationship between age and average total sleep time ATST. TO obtain a measure for ATST (in minutes), recordings were taken on each subject on three consecutive nights and then averaged. The results are displayed as follows. ATST(in minutes) Age (YEARS) 586

Answer 1

solution - To obtain a measure for ATST recordings were taken on each subject on three consecutive nights and then averaged. The result are displayed belows. Hi (Age (years) T 4 (ATT) Gminutes) Yi (ATST) (inminutes) 212 586 16 462 196 100 niyi 2344 6468 4910 4520 5313 5320 5927.2 34802.2 491 sos 462 S32 64 11.5 10 132.25 100 153.76 762.01 12.4 Eni= 69.9 n=7 478 241 =3576 the simple linear regression line is Here, ßo and ßi are intercept and method of least square are used and Bi parameters. Then estimated Yra Bot Bini slope parameters. The to estimate these bo regression line is, ý j = Bot ßi ai where, B = and Ediyi- (Exi) (Eyi)%. Exi2 - (221)2/n Bo = - B . B = 34802. 2 - (og,g) (3576)/2 762.01- (69.922/7 B = 3480212 - 35708-9142 762101 - 698.0014 -14.1655 3 =

ŷ - Eyi = 3576 = 510.8571 * = 59,9 - 9.9 852 Bo = 510.8571-(-14.1655) (9.9857) Bo = 652.3095 Then estimated regression line is }; = Bot Bili - i = 652.3095 + (-14.1655) ai 19 = 652.3095-(411655) xi | to estimate the ATST when use age the regression line = 1015 je a=1015 Then, regression line becomes, ŷ = 652.3095 - (14.1655) (10.5) Ti = 503.5?17 / Then estimateda value of y = 503.5717 when a=los