Question

3£®Ä³µØËæמ­¼ÃµÄ·¢Õ¹£¬¾ÓÃñÊÕÈëÖðÄêÔö³¤£¬Ï±íÊǸõØÒ»½¨ÉèÒøÐÐÁ¬ÐøÎåÄêµÄ´¢Ðî´æ¿î£¨Äêµ×Óà¶î£©£¬Èç±í1£º

Äê·Ýx	2011	2012	2013	2014	2015
´¢Ðî´æ¿îy£¨Ç§ÒÚÔª£©	5	6	7	8	10

ΪÁËÑо¿¼ÆËãµÄ·½±ã£¬¹¤×÷ÈËÔ±½«ÉϱíµÄÊý¾Ý½øÐÐÁË´¦Àí£¬t=x-2010£¬z=y-5µÃµ½Ï±í2£º

ʱ¼ä´úºÅt	1	2	3	4	5
z	0	1	2	3	5

£¨¢ñ£©Çóz¹ØÓÚtµÄÏßÐԻع鷽³Ì£»
£¨¢ò£©ÓÃËùÇó»Ø¹é·½³ÌÔ¤²âµ½2020ÄêÄêµ×£¬¸ÃµØ´¢Ðî´æ¿î¶î¿É´ï¶àÉÙ£¿
£¨¸½£º¶ÔÓÚÏßÐԻع鷽³Ì$\hat y=\hat bx+\hat a$£¬ÆäÖÐ$\widehat{b}$=$\frac{\sum_{i=1}^{n}{x}_{i}{y}_{i}-n\overline{x}•\overline{y}}{\sum_{i=1}^{n}{{x}_{i}}^{2}-n{\overline{x}}^{2}}$£¬$\widehat{a}$=$\overline{y}$-$\widehat{b}$$\overline{x}$£©

Answer 1

·ÖÎö £¨¢ñ£©ÓɱíÖеÄÊý¾Ý·Ö±ð¼ÆË㣬¼´¿Éд³öÏßÐԻع鷽³Ì£»
£¨¢ò£©t=x-2010£¬z=y-5£¬´úÈëz=1.2t-1.4µÃµ½£ºy-5=1.2£¨x-2010£©-1.4£¬¼´y=1.2x-2408.4£¬¼ÆËãx=2020ʱ£¬µÄÖµ¼´¿É£®

½â´ð ½â£º£¨¢ñ£©$\overline t=3£¬\overline z=2.2$$\sum_{i=1}^5{t_i}{z_i}=45$£¬$\sum_{i=1}^5{{t_i}^2}=55$£¬$\hat b=\frac{45-5¡Á3¡Á2.2}{55-5¡Á9}=1.2$£¬$\hat a=\overline z-b\overline t=2.2-3¡Á1.2=-1.4$£¬
¡àz=1.2t-1.4£»
£¨2£©t=x-2010£¬z=y-5£¬´úÈëz=1.2t-1.4µÃµ½£ºy-5=1.2£¨x-2010£©-1.4£¬¼´y=1.2x-2408.4£¬
¡ày=1.2¡Á2020-2408.4=15.6£¬¡àÔ¤²âµ½2020ÄêÄêµ×£¬¸ÃµØ´¢Ðî´æ¿î¶î¿É´ï15.6ǧÒÚÔª£®

µãÆÀ ±¾Ì⿼²éÁËÇóÏßÐԻع鷽³ÌµÄÓ¦ÓÃÎÊÌ⣬Ҳ¿¼²éÁËÀûÓÃÏßÐԻع鷽³ÌÔ¤²âÉú²úÎÊÌ⣬ÊÇ»ù´¡ÌâÄ¿£®