问题 问答题

简述最小二乘法。

答案

参考答案:如果Y为观察数据值,[*]为方程的估算值,则估算误差可表示为:
[*]
人们通常将误差表示成平方和形式,由于共有n组关于X和Y的数据,每一个y都会有一个误差,所以得到误差的平方和为:
[*]
如果采用下列方程组估算回归方程的参数,则可使上述误差的平方和为最小,这种估算回归方程参数的方法,被称为最小二乘法,即:
[*]
式中:n、∑X、∑Y、∑XY、∑X2是从n组关于X和Y的观察数据中得来的,所以都是已知的,利用公式可以求出方程中的a、b两个参数值。

阅读理解

It was Mother’s Day morning last year and I was doing my shopping at our local supermarket with my five-year-old son, Tenyson. As we were leaving, we found that only minutes earlier an elderly woman had fallen over at the entrance and had hit her head on the concrete. Her husband was with her, but there was blood everywhere and the woman was embarrassed and clearly in shock.

Walking towards the scene, Tenyson became very upset about what had happened to the couple. He said to me, “Mum, it’s not much fun falling over in front of everyone.”

At the front of the supermarket a charity(慈善) group had set up a stand selling cooked sausages and flowers to raise funds. Tenyson suggested that we should buy the lady a flower. “It will make her feel better,” he said. I was amazed that he’d come up with such a sweet idea. So we went over to the flower seller and asked her if we could buy a flower for the lady to cheer her up. “Just take it,” she replied. “I can’t take your money for such a wonderful gesture.”

By now paramedics(救援人员)had arrived, and were attending the injured woman. As we walked up to her, my son became intimidated by all the blood and medical equipment. He said he was just too scared to go up to her.

Instead I gave the flower to the woman’s husband and told him, “ My son was very upset for your wife and wanted to give her this flower to make her feel better.”

At that, the old man started crying and said, “Thank you so much, you have a wonderful son. Happy Mother’s Day to you.”

The man then bent down and gave his wife the flower, telling her who it was from. Though badly hurt and shaken, the old lady looked up at Tenyson with love in her eyes and gave him a little smile.

小题1:What dose the author intend to tell us?

A.One can never be too careful.

B.Actions speak louder than words.

C.Love begins with a little smile.

D.A small act of kindness brings a great joy.小题2:Which of the following is TRUE according to the passage?

A.The elderly woman was knocked down by Tenyson.

B.Tenyson’s idea of buying a flower gained his father’s support.

C.Tenyson’s care for the elderly woman puzzled the flower seller.

D.The elderly woman was moved to tears by Tenyson’s gesture.小题3:The underlined word “intimidated” in the fourth paragraph probably means “___________”.

A.astonished

B.struck

C.frightened

D.excited小题4:What would be the best title for the passage?

A.Flower Power

B.Mother’s Day

C.An Accidental Injury

D.An Embarrassing Moment

单项选择题