statistics 急問!!!!! [復制鏈接]

(Pindyck and Rubinfeld, Exercise 3.7)
Suppose that you are attempting to
build a linear regression model that explains aggregate savings behaviour as a function of the level
of interest rates. Would you rather sample during a period of fluctuating interest rates or a period
in which interest rates were relatively constant? Explain.


St = β0 + β1 rt + εt

(Hint: you may wish to look at the formula for the variance of the estimator for β1)


我唔明佢做緊D咩?有冇好友可以講下..

引用第18樓Bun於2010-01-27 20:40發表的“”:
sigma^2 係var(Y)姐係Var(β0 + β1 rt + εt)
姐係Var(εt)...因為β0 同 β1 rt係constant
MSE係D DATA既mean square error...姐係d data同條regression line之間既error....
我地做緊既野係收到好多DATA....然後就fit一條線...呢條線既特點就係minize個MSE...
答返你條問題...
其實佢個fluctuate X姐係令到我拎返黎果D X既range大D(每個X有1個respond)...
咁當然拎返黎既X個range越大...就自然fit到條好D既線....
↑如果你想知點解你再覆我= =因為要用圖先解得明....我懶畫圖:P
.......

因為我記憶中的Var(b1)是MSE/SXX
X的Fluctate同時令y fluctate
變成MSE跟SXX的角力-.-"

要是數式是sigma^2/SXX
問完之後就明了

我猜, MSE應該係estimator of sigma^2

引用第13樓victorally於2010-01-27 13:15發表的“”:
誠心一問
sigma^2 同 εt有關架咩?
即係x 點fluctuate, MSE都不變嗎...?
(雖然我都覺得fluctuate "比較"似答案)
.......

首先搞返清楚先...

sigma^2 係var(Y)姐係Var(β0 + β1 rt + εt)
姐係Var(εt)...因為β0 同 β1 rt係constant

MSE係D DATA既mean square error...姐係d data同條regression line之間既error....
我地做緊既野係收到好多DATA....然後就fit一條線...呢條線既特點就係minize個MSE...

答返你條問題...
其實佢個fluctuate X姐係令到我拎返黎果D X既range大D(每個X有1個respond)...
咁當然拎返黎既X個range越大...就自然fit到條好D既線....
↑如果你想知點解你再覆我= =因為要用圖先解得明....我懶畫圖:P

引用第16樓Bun於2010-01-27 20:28發表的“”:
你PM你email或者MSN比我啦= ="

have already pm la...thz!!

引用第14樓sy0250358於2010-01-27 20:20發表的“”:
咁我想請問你有冇果VAR(a) 果proof?? [表情] [表情]
即係,
Var[a] = (sigma^2 )*[summation([Xi]^2) ]/ [summation[(Xi-mean of X)^2]] * n
.......

你PM你email或者MSN比我啦= ="

引用第11樓sy0250358於2010-01-27 12:19發表的“”:
Q: In the lecture we have computed Var(ˆb) under the assumption that ‾ϵ = 0.
Show that such an assumption can be removed without affecting the final result.
.......

下...唔明佢問咩喎..... Var(ˆb) 條式只係關於Var(ϵ )之MA...都唔關 ‾ϵ 事= =...
咁佢 emove左自然冇問題....
呢個assumption只係用黎令條regression冇bias....

都係果句...我怕我記錯:P

引用第8樓Bun於2010-01-27 01:41發表的“”:
不過如果你想要Var of β1既proof...我諗你可以自己上網搵= =或者搵我= =""
我可以比D NOTES你睇....
因為要講好多野..太長...打唔到係度~~

咁我想請問你有冇果VAR(a) 果proof??
即係,
Var[a] = (sigma^2 )*[summation([Xi]^2) ]/ [summation[(Xi-mean of X)^2]] * n


其實我唔知點樣PROOF...

引用第7樓Bun於2010-01-27 01:39發表的“”:
Var( β1)=sigma^2/SXX             sigma^2 係εt係Variance
咁而家X係interest rate...
所以如果fluctuating interest rates 既話...SXX會大左...
咁個VARIANCE OF β1就會細左....
.......

誠心一問
sigma^2 同 εt有關架咩?
即係x 點fluctuate, MSE都不變嗎...?
(雖然我都覺得fluctuate "比較"似答案)

對唔住, 已經好幾年
notes應該有排搵

引用第8樓Bun於2010-01-27 01:41發表的“”:
不過如果你想要Var of β1既proof...我諗你可以自己上網搵= =或者搵我= =""
我可以比D NOTES你睇....
因為要講好多野..太長...打唔到係度~~

可否PMPM THX大大

引用第8樓Bun於2010-01-27 01:41發表的“”:
不過如果你想要Var of β1既proof...我諗你可以自己上網搵= =或者搵我= =""
我可以比D NOTES你睇....
因為要講好多野..太長...打唔到係度~~

Q: In the lecture we have computed Var(ˆb) under the assumption that ‾ϵ = 0.
Show that such an assumption can be removed without affecting the final result.


其實仲有條問題, 我知道VAR(B)果PROOF..但係佢用左ASSUME ‾ϵ = 0.
上面條問題就要我Show that such an assumption can be removed without affecting the final result, 可以點做?

引用第6樓victorally於2010-01-27 00:12發表的“”:
Var(β1) = (MSE) / [summation(Xi-mean of X)^2]
唔...好難話好唔好架wo...好多因素影響
data集唔集中都會有REGRESSION line出到黎
.......

咁應該揀邊個呀..定係要DEPEND 係咩情況??

引用第6樓victorally於2010-01-27 00:12發表的“”:
Var(β1) = (MSE) / [summation(Xi-mean of X)^2]
唔...好難話好唔好架wo...好多因素影響
data集唔集中都會有REGRESSION line出到黎
.......

university level...

不過如果你想要Var of β1既proof...我諗你可以自己上網搵= =或者搵我= =""
我可以比D NOTES你睇....
因為要講好多野..太長...打唔到係度~~

應該係咁....
define 幾樣野方便D...
1 .) Assume there are i th data
2 .) Let SXX=summation of (Xi-mean(X)) for all i.

咁如果你有讀過linear regression...會知道
Var( β1)=sigma^2/SXX                   sigma^2 係εt係Variance
咁而家X係interest rate...
所以如果fluctuating interest rates 既話...SXX會大左...
咁個VARIANCE OF β1就會細左....

所以如果想拎個好既β1....就要拎D fluctuating 既interest rates

年幾前讀既course= =希望冇記錯...

引用第5樓sy0250358於2010-01-26 22:57發表的“”:
我想問咩叫formula for the variance of the estimator for β1..
係咪即話
Var(β1) = (sigma^2) / [summation(Xi-mean of X)^2]   ??
.......

Var(β1) = (MSE) / [summation(Xi-mean of X)^2]

唔...好難話好唔好架wo...好多因素影響
data集唔集中都會有REGRESSION line出到黎
最重要對應個Y準唔準*-*


fluctate 點 , MSE大點, variance of b1又會大d, prediction interval 亦會大
簡單講, 即係你個b1亦都同現實偏差大點
不過, 最重要對應個Y準唔準

請問呢條係咩程度既題目