土豆泥
draw a simple graph illustrating a violation of the following assumptions
concerning the residuals е, εi~ N(0,σ²) for all i.
如果y轴表示е的话，x轴用什莫来表示才好才能表示没有满足题目要求的假设呢，大概
的是个什莫形状的图形呢？
谢谢
neige
there are more than one assumption in that statement, which one do you want to verify?
土豆泥
这道题不是要来用图证明满足这个假设,而且是图表示出如果不满足u=0,variance are not constant情况下是哪种图.其实我也是一直困惑,这是两个条件,一个是u=0,另一个是variance are not constant,如果用简单的图来表示出来呢?
[quote]引用第1楼neige于2008-04-30 06:30发表的“”:
there are more than one assumption in that statement, which one do you want to verify?[/quote]
javier
[quote]引用第0楼土豆泥于2008-04-29 23:13发表的“如何简单的画这个图”:
draw a simple graph illustrating a violation of the following assumptions
concerning the residuals е, εi~ N(0,σ²) for all i.
如果y轴表示е的话，x轴用什莫来表示才好才能表示没有满足题目要求的假设呢，大概
的是个什莫形状的图形呢？
.......[/quote]
一个图不是很容易。
1. 想看是不是均值为零，几乎不可能。最好是做均值等于0的检验。
2. 如果是回归的残差，可以画残差图： plot e vs yhat. 然后有没有明显的模式。如果基本上均匀分布在-1
到1之间，基本上可以认为是同方差的，而且均值接近于0
3. 关于正态的假设，可以画QQ图。
参阅 程晞如 王松桂的《近代回归分析》或者其他类似的书。
JaneQ
" draw a simple graph illustrating a violation of the following assumptions
concerning the residuals е, ~ N(0,σ²) for all i."
It seems that you need to check the standard assumptions of regression residuals
1) εi's are independent (independence assumption)
2) εi has a normal distribution (normality assumption)
3) εi's have equal variance (equal-variance assumption)
In that case, the σ² is unknown, please check any book on regression for detailed methods about how to check the assumptions.
If you have to use a single graph to illustrate the assumptions, you may look the εis as a random sample, get a density histogram of the residuals (εis) and superimpose the density of N(0,s²), where s² is the sample variance.
JaneQ
Note:
You don't have to verify mu=0 because the residuals will always have the mean be 0 in standard linear regression.
