(1)散点图略;
(2)Ⅰ.先把数据列成表:
项目 品牌
| 热量百分比x
| 品味记录y
| x2
| y2
| xy
|
1
| 25
| 89
| 625
| 7 921
| 2 225
|
2
| 34
| 89
| 1 156
| 7 921
| 3 026
|
3
| 20
| 80
| 400
| 6 400
| 1 600
|
4
| 19
| 78
| 361
| 6 084
| 1 482
|
5
| 26
| 75
| 676
| 5 625
| 1 950
|
6
| 20
| 71
| 400
| 5 041
| 1 420
|
7
| 19
| 65
| 361
| 4 225
| 1 235
|
8
| 24
| 62
| 576
| 3 844
| 1 488
|
∑
| 187
| 609
| 4 555
| 47 06
| 14 426
|
Ⅱ.计算b,a的值:
由上表分别计算x,y的平均数得
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823125731078194.gif)
=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823125731094290.gif)
,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823125731109199.gif)
=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823125731140320.gif)
,代入公式
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231257312341105.gif)
,得(注意:不必把
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823125731078194.gif)
=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823125731094290.gif)
,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823125731109199.gif)
=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823125731140320.gif)
化为小数,以减小误差)
b=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231257313741605.gif)
=1.036710,
a=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823125731140320.gif)
-1.036 710×
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823125731094290.gif)
="76.125-24.233" 1="51.891" 9.
Ⅲ.写出回归直线方程
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823125731421298.gif)
=51.9+1.037x.
(3)回归直线方程
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823125731421298.gif)
=51.9+1.037x中的回归系数b=1.037,它的意义是:热量比每增加一个百分比,口味记录平均增加1.037分.
(4)人们之所以喜欢吃位于回归直线上方的饼干而不是下方的饼干,是因为饼干所含有的热量百分比相同时,人们的满意率比较高;并且满意率相同时,位于回归直线上方的饼干所含有热量百分比较低,人们比较喜欢吃热量百分比较低的食品.