问题 解答题
某兴趣小组欲研究昼夜温差大小与患感冒人数多少之间的关系,他们分别到气象局与某医院抄录了1至6月份每月10号的昼夜温差情况与因患感冒而就诊的人数,得到如下资料:
日期1月10日2月10日3月10日4月10日5月10日6月10日
昼夜温差x(℃)1011131286
就诊人数y(人)222529261612
该兴趣小组确定的研究方案是:先从这六组数据中选取2组,用剩下的4组数据求线性回归方程,再用被选取的2组数据进行检验.
(Ⅰ)求选取的2组数据恰好是相邻两个月的概率;
(Ⅱ)若选取的是1月与6月的两组数据,请根据2至5月份的数据,求出y关于x的线性回归方程y=bx+a;
(Ⅲ)若由线性回归方程得到的估计数据与所选出的检验数据的误差均不超过2人,则认为得到的线性回归方程是理想的,试问该小组所得线性回归方程是否理想?
答案

(Ⅰ)由题意知本题是一个古典概型,

设抽到相邻两个月的数据为事件A

试验发生包含的事件是从6组数据中选取2组数据共有C62=15种情况,

每种情况都是等可能出现的其中,

满足条件的事件是抽到相邻两个月的数据的情况有5种

P(A)=

5
15
=
1
3

(Ⅱ)由数据求得

.
x
=11,
.
y
=24

由公式求得b=

18
7

再由

.
a
=
.
y
-b
.
x
求得a=-
30
7

∴y关于x的线性回归方程为y¯=

18
7
x-
30
7

(Ⅲ)当x=10时,y=

150
7
,|
150
7
-22
|=
1
3
<2

∴该小组所得线性回归方程是理想的.

阅读理解

Last night I had the best gift ever.

My older son was reading a detective novel while my younger son was reading fairy tales. They were each in different rooms, engrossed in their books with no TV, music or anything else distracting (使分心) their attention.

I read a lot during my childhood, curling (蜷缩) up in sofa or lying in bed. Like anyone else, I had lots of other interests, but once I discovered reading, I really enjoyed it. I read everything — books, magazines, newspapers, even the back of food packages if there was nothing else to read at the moment. I must thank my parents for their love of reading. Longing for more information and knowledge, my parents were always reading a lot.

Today’s children are provided with a variety of choices. It is so easy for them to become uninterested in reading and to view it as boring, uncool and unnecessary. There are TVs with astonishing choices of programs; there are MP3 players with thousands of songs at their fingertips; there are the Internet and mobile phones.

I’ve told my sons that reading comes with information, understanding and connection, each of which will help them at every stage in their lives now and forever. So when my sons were reading their books last night, I watched them, noticing them put a bookmark into their books. That’s the most amazing gift that I have ever received.

小题1:The best title for this passage is _____.

A.My Two Sons

B.An Amazing Gift

C.My Favorite, Reading

D.Let’s Read Together小题2:The phrase “engrossed in” in the second paragraph can be replaced by “_____”.

A.connected by

B.separated by

C.devoted to

D.worried about小题3:What does the author think of TVs, MP3 players, the Internet and mobile phones?

A.They are boring, uncool and unnecessary.

B.They are too expensive for a family to afford.

C.They might distract children’s attention.

D.They might enrich children’s lives and make them happy.小题4:According to the passage, the author’s best gift is _____.

A.her sons’ love for reading

B.reading books alone

C.bookmarks from her sons

D.having a happy family

问答题