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real__yu · 2025年02月07日

RSS(R)

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NO.PZ202001080100002602

问题如下:

b. What is the R2,R2R^2, \overline\R^2, and F statistic of this regression?

选项:

解释:

So, the TSS = 75.797 and the ESS = 68.598.

R2=ESS/TSS=68.598/75.797=90.5%R^2=ESS/TSS=68.598/75.797=90.5\%

R2=1n1nk1(1R2)=11011021(10.905)=0.878\overline R^2=1-\frac{n-1}{n-k-1}(1-R^2)=1-\frac{10-1}{10-2-1}(1-0.905)=0.878

F=(RSSRRSSU)/qRSSU/(NkU1)=(7.580.72)/20.72/(1021)=33.47F=\frac{(RSS_R-RSS_U)/q}{RSS_U/(N-k_U-1)}=\frac{(7.58-0.72)/2}{0.72/(10-2-1)}=33.47

请问RSS(R)怎么算出来的?

1 个答案

李坏_品职助教 · 2025年02月07日

嗨,努力学习的PZer你好:


这一列求出来是∑(y-y_)^2 = 75.797,而RSS_R指的是restricted RSS,这个就是总的残差平方和 = 1/n * ∑(y-y_)^2 = 75.797/10 = 7.58.


而RSS_U指的是unrestricted RSS,这个是1/n *(TSS - ESS) = 0.72.

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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NO.PZ202001080100002602 问题如下 Whis the R2,R‾2R^2, \overline\R^2R2,R2, anF statistic of this regression? So, the TSS = 75.797 anthe ESS = 68.598. R2=ESS/TSS=68.598/75.797=90.5%R^2=ESS/TSS=68.598/75.797=90.5\%R2=ESS/TSS=68.598/75.797=90.5%R‾2=1−n−1n−k−1(1−R2)=1−10−110−2−1(1−0.905)=0.878\overline R^2=1-\frac{n-1}{n-k-1}(1-R^2)=1-\frac{10-1}{10-2-1}(1-0.905)=0.878R2=1−n−k−1n−1​(1−R2)=1−10−2−110−1​(1−0.905)=0.878F=(RSSR−RSSU)/qRSSU/(N−kU−1)=(7.58−0.72)/20.72/(10−2−1)=33.47F=\frac{(RSS_R-RSS_U)/q}{RSS_U/(N-k_U-1)}=\frac{(7.58-0.72)/2}{0.72/(10-2-1)}=33.47F=RSSU​/(N−kU​−1)(RSSR​−RSSU​)/q​=0.72/(10−2−1)(7.58−0.72)/2​=33.47 这题的知识点在哪讲过啊

2024-05-09 19:42 1 · 回答

NO.PZ202001080100002602 问题如下 Whis the R2,R‾2R^2, \overline\R^2R2,R2, anF statistic of this regression? So, the TSS = 75.797 anthe ESS = 68.598. R2=ESS/TSS=68.598/75.797=90.5%R^2=ESS/TSS=68.598/75.797=90.5\%R2=ESS/TSS=68.598/75.797=90.5%R‾2=1−n−1n−k−1(1−R2)=1−10−110−2−1(1−0.905)=0.878\overline R^2=1-\frac{n-1}{n-k-1}(1-R^2)=1-\frac{10-1}{10-2-1}(1-0.905)=0.878R2=1−n−k−1n−1​(1−R2)=1−10−2−110−1​(1−0.905)=0.878F=(RSSR−RSSU)/qRSSU/(N−kU−1)=(7.58−0.72)/20.72/(10−2−1)=33.47F=\frac{(RSS_R-RSS_U)/q}{RSS_U/(N-k_U-1)}=\frac{(7.58-0.72)/2}{0.72/(10-2-1)}=33.47F=RSSU​/(N−kU​−1)(RSSR​−RSSU​)/q​=0.72/(10−2−1)(7.58−0.72)/2​=33.47 这个F的计算公式需要掌握吗

2023-01-07 11:18 1 · 回答