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# 統計 計量 迴歸分析

1/Y=B1+B2X+U

Y 86 79 76 69 65 62 52 51 51 48

X 3 7 12 17 25 35 45 55 70 120

a.what is the interpretation of B2?

b.what is the rate of change of Y with respect X?

c.what is the elasticity of Y with respect to X?

for the same data .run the regression

Y=B1+B2(1/X)+U

e.can you compare the r-square of the two model ?why or why not?

f.how do you decide which is a better model?

麻煩統計高手~謝謝..

### 2 Answers

- 1 decade agoFavorite Answer
1/Y=B1+B2X+U

a.what is the interpretation of B2?

[回]

X 增加一單位, 對 1/Y 的影響.

若 1/Y 沒有實務意義, 實在很難解釋.

b.what is the rate of change of Y with respect X?

[回]

要問的應是 dY/dX, 或更正確地說, 是 dY^/dX, 其中 Y^ =B1+B2 X.

用隱函數微分 (忽略 U),

dY/dX (-1/Y^2) = B2. 故 dY/dX = -B2 Y^2.

若 1/Y 沒有實務意義, B2 的解釋應根據這結果.

c.what is the elasticity of Y with respect to X?

[回]

"the elasticity of Y with respect to X" 應該是 (ΔY/Y)/(ΔX/X)?

如果是的話, 以微分來表示, 就是 (dY/dX)/(Y/X) = (dY/dX)(X/Y).

把 b. 的結果套進去計算就是了.

for the same data .run the regression

Y=B1+B2(1/X)+U

e.can you compare the r-square of the two model ?why or why not?

[回]

不可!

一個是 1/Y 的變異的解釋問題, 一個是 Y 的變異的解釋問題,

兩者比較並無意義.

f.how do you decide which is a better model?

[回]

如果目的是解釋或預測 Y, 則應以 Y 為共同比較基礎.

因此, 可以分別計算兩個模型的 Y-hat, 依次以 y1, y2 表示之.

然後比較 Y-y1 與 Y-y2. 不過, 以甚麼方式綜合比較這許多

殘差 (Y-y1 與 Y-y2) 則無定論. 或許可考慮 "平均殘差"

Σ|Y-y1|/n 與 Σ|Y-y2|/n, 或者用總和相對殘差 Σ(|Y-y1|/Y)

與 Σ(|Y-y2|/Y), 均方根相對殘差 (1/n)√Σ(|Y-y1|/Y)^2 與

(1/n)√Σ(|Y-y2|/Y)^2 等, 可依研究目的決定之. 以上未考慮

均方殘差 Σ(Y-y1)^2 與 Σ(Y-y2)^2, 因在 fit models 時分別

採用最小平方法, 後者一定最小. 若比較 Σ(1/Y-1/y1)^2 與

Σ(1/Y-1/y2)^2 則剛好相反: 前者最小.