Question

4£®Ä³Ð£ÎªÁËÑ¡°ÎѧÉú²Î¼ÓÌåÓý±ÈÈü£¬¶Ô5ÃûѧÉúµÄÌåÄܺÍÐÄÀí½øÐÐÁ˲âÆÀ£¬³É¼¨£¨µ¥Î»£º·Ö£©ÈçÏÂ±í£º

ѧÉú±àºÅi	1	2	3	4	5
ÌåÄܳɼ¨x	80	75	70	65	60
ÐÄÀí³É¼¨y	70	66	68	64	62

£¨1£©ÔÚ±¾´Î²âÆÀÖУ¬¹æ¶¨ÌåÄܳɼ¨70·ÖÒÔÉÏ£¨º¬70·Ö£©ÇÒÐÄÀí³É¼¨65·ÖÒÔÉÏ£¨º¬65·Ö£©ÎªÓÅÐã³É¼¨£¬´ÓÕâ5ÃûѧÉúÖÐÈÎÒâ³éÈ¡2ÃûѧÉú£¬ÉèX±íʾ³É¼¨ÓÅÐãµÄѧÉúÈËÊý£¬ÇóXµÄ·Ö²¼ÁкÍÊýѧÆÚÍû£»
£¨2£©¼ÙÉèѧÉúµÄÌåÄܳɼ¨ºÍÐÄÀí³É¼¨¾ßÓÐÏßÐÔÏà¹Ø¹Øϵ£¬¸ù¾ÝÉϱíÀûÓÃ×îС¶þ³Ë·¨£¬ÇóyÓëxµÄ»Ø¹éÖ±Ïß·½³Ì£¬£¨²Î¿¼Êý¾Ý£º$\underset{\stackrel{5}{¡Æ}}{i=1}$x_iy_i=23190£¬$\underset{\stackrel{5}{¡Æ}}{i=1}$x_i²=24750£©£®

Answer 1

·ÖÎö £¨1£©ÓÉÌâÒâµÃ1ºÅѧÉú¡¢2ºÅѧÉú¡¢3ºÅѧÉúΪÓÅÐã³É¼¨£¬ÁíÍâÁ½ÃûѧÉú²»ÊÇÓÅÐã³É¼¨£¬´Ó¶øµÃµ½XµÄ¿ÉÄÜȡֵΪ0£¬1£¬2£¬·Ö±ðÇó³öÏàÓ¦µÄ¸ÅÂÊ£¬ÓÉ´ËÄÜÇó³öXµÄ·Ö²¼ÁкÍÊýѧÆÚÍû£®
£¨2£©ÀûÓÃ×îС¶þ³Ë·¨·Ö±ðÇó³ö$\widehat{b}$£¬$\widehat{a}$£¬ÓÉ´ËÄÜÇó³öyÓëxµÄ»Ø¹éÖ±Ïß·½³Ì£®

½â´ð ½â£º£¨1£©ÓÉÌâÒâµÃ1ºÅѧÉú¡¢2ºÅѧÉú¡¢3ºÅѧÉúΪÓÅÐã³É¼¨£¬ÁíÍâÁ½ÃûѧÉú²»ÊÇÓÅÐã³É¼¨£¬
´Ó¶øµÃµ½XµÄ¿ÉÄÜȡֵΪ0£¬1£¬2£¬
P£¨X=0£©=$\frac{{C}_{2}^{2}}{{C}_{5}^{2}}$=$\frac{1}{10}$£¬
P£¨X=1£©=$\frac{{C}_{3}^{1}{C}_{2}^{1}}{{C}_{5}^{2}}$=$\frac{6}{10}$£¬
P£¨X=2£©=$\frac{{C}_{3}^{2}}{{C}_{5}^{2}}$=$\frac{3}{10}$£¬
¡àXµÄ·Ö²¼ÁÐΪ£º

X	0	1	2
P	$\frac{1}{10}$	$\frac{6}{10}$	$\frac{3}{10}$

EX=$0¡Á\frac{1}{10}+1¡Á\frac{6}{10}+2¡Á\frac{3}{10}$=$\frac{6}{5}$£®
£¨2£©¡ß$\overline{x}$=$\frac{1}{5}$£¨80+75+70+65+60£©=70£¬$\overline{y}$=$\frac{1}{5}$£¨70+66+68+64+62£©=66£¬
$\underset{\stackrel{5}{¡Æ}}{i=1}$x_iy_i=23190£¬$\underset{\stackrel{5}{¡Æ}}{i=1}$x_i²=24750£¬
¡à$\widehat{b}$=£¨$\sum_{i=1}^{5}{x}_{i}{y}_{i}$-5$\overline{x}\overline{y}$£©¡Â£¨$\sum_{n=1}^{5}{{x}_{i}}^{2}-5{\overline{x}}^{2}$£©
=$\frac{23190-5¡Á70¡Á66}{24750-5¡Á7{0}^{2}}$
=$\frac{90}{250}$=0.36£¬
$\widehat{a}$=$\overline{y}-\widehat{b}\overline{x}$=66-0.36¡Á70=40.8£¬
¡àyÓëxµÄ»Ø¹éÖ±Ïß·½³ÌΪ$\widehat{y}$=0.36x+40.8£®

µãÆÀ ±¾Ì⿼²éÀëÉ¢ÐÍËæ»ú±äÁ¿µÄ·Ö²¼ÁкÍÊýѧÆÚÍûµÄÇ󷨣¬¿¼²é»Ø¹éÖ±Ïß·½³ÌµÄÇ󷨣¬ÊÇÖеµÌ⣬½âÌâʱҪÈÏÕæÉóÌ⣬עÒâ×îС¶þ³Ë·¨µÄºÏÀíÔËÓã®