W01 課程介紹

2025-09-10-Wednesday 14:10-17:00 林師模教授 shihmolin@gmail.com (助教Sopia張桂鳳)

W02 Review of Statistics

2025-09-17-Tuesday 14:00-17:00 林師模教授

W03 --本週課目標題--

2025-09-24-Tuesday 14:00-17:00 林師模教授

■ Hypothesis testing, ■ANOVA(Analysis of variance) 變異數分析;
ChatGPT說明 The steps of hypothesis
例如: 100學生數學成績，內有分N M S 北中南三區學生
1.what question? is region -> effect of math score.
2.H0: μ1=μ2=μ3 (μN=μM=μS)
H1: μ1≠μ2≠μ3 either one ≠
3.★ select Test Statistic 檢定統計量 -找出critical value. (to know the test statistic)
if the statistic not greater than critical value, fall in acceptance area, means that you can not reject the H0.
- 如何找出test方法 經驗/自己推導-想辦法試驗/如果你不知道-you can develop by yourself or even you can publish/ or use other people’s way, to know how others usely do/.
- 多看別人的,多看文章,多看案例.
- ★ need to know what would be the porbability distribution (with your test)
4. Collect Data and Calculate the Test Statistic
- need dicide alpha: significant value first (0.05 or 0.01, 0.10..)
consulting (F) talbe, then you can find out the coreponding critical value.
★ Alpha value 的意義: TypeI error: Ho is true the probability of rejecting the null only 5% (alpha) 你決定了alpha值，就是你決定可能犯了型1錯誤的機率，在alpha值之內。

5. Find the Critical Value(s) or p-value
   
6. Make a Decision
   
7. State the Conclusion

■ANOVA(Analysis of variance)
if we have three or more normal distribution, and we would like to know whether their means are the same or not?
比如剛剛那來自三個地區的100個學生，是否 H 可以求出一個total mean = μ
對任一個 (Yij-μ) = (Ynj-μj) + (μj-μ) 對所有n點想要總和，需要先square以免被相互抵銷
所以先 sauare (Yij-μ) 全部加總起來

SST (sum square total) = SSE (error sum of square 你自己母體的差) + SSB (between group -sum square) 有時SSE 也叫做 SSW (Within group seim square 的意思)
SST=SSE+SSB
如果各組差異大，那麼SSB會變大。 所以如果兩邊都除以SST 這樣就成了
1= (SSE/SST) + (SSB/SST) 假設 這是 1=0.3 + 0.7 那你怎麼知道 0.7有沒大過critical value?
如果各組差異大，那麼SSB會變大。 所以如果兩邊都除以SST 這樣就成了
1= (SSE/SST) + (SSB/SST) 假設 這是 1=0.3 + 0.7 那你怎麼知道 0.7有沒大過critical value?

問Gemini20250924
SST(sum square total), SSE (error sum of square), SSB (between group -sum square)
設SST=SSE+SSB 所以 1= (SSE/SST) + (SSB/SST)
假如 SSE=0.3 而 SST=0.7 那要怎麼知道 0.7有沒大過critical value?

F Statistical calculation step:
F 統計量的計算公式通常是指變異數分析（ANOVA）中的 F = MSB / MSW，
其中MSB 是組間平均平方（Mean Square Between），
MSW 是組內平均平方（Mean Square Within），
F 值用於檢定多個母體平均數是否完全相同。

■ wiki F檢定
F 統計量的計算步驟
計算組間平方和(SSB)：: 衡量不同組別之間的平均變異。
計算組內平方和(SSW)：: 衡量每個組別內部數據點與該組平均數之間的變異。
計算自由度(df)：:
組間自由度(dfB) = 組別數量- 1
組內自由度(dfW) = 總樣本數- 組別數量 (但老師在這個例題，用的是n-1 不是n-group number 因為是SST,但注意📌)
計算平均平方(MS)：: 組間平均平方(MSB) = SSB / dfB
組內平均平方(MSW) = SSW / dfW
計算F 值：: F = MSB / MSW。
應用情境
變異數分析(ANOVA)：: 這是F 統計量最常被使用的情境，用於比較三個或三個以上群體平均數的差異。
變異數比率檢定：: F 檢定也可以用於檢定兩個母體變異數是否相等。
如何理解F 值
F 值是組間變異與組內變異的比例。
較大的F 值表示組間的平均差異比組內的平均差異大，這暗示著群體平均數之間存在顯著差異。
📌注意: 正式用的是SSB /SSW 不是SST (SSW/m3 這個m3 就是df 就是 n-組別數量 )

F = (SSB/(J-a)) / (SSW/(n-J)) 老師說:根據經驗 n=100 J=3 時 Falpha .=.3 但如果J=5 可能小於3, 如果J=10 會更小。 不信去查F表。 F表最上面那行是group的df, 左邊直行是n的df。

老師要教。怎樣用excel去做F test data資料 –> data analysis資料分析 單因子變異數分析 –> by row 逐列: @回家用googlesheet 做看看。

ANOVA如果有 2 factor(如男女)但 sample數都一樣，叫做balanced table如果 sample數不一樣就是imbalanced table (如果每一類只有1個sample data)叫做non-repetitions experiment非重複實驗 HomeWork:
老師出一個作業下週三以前sumit report, 題目是: 自己設計question自己收集data 做一個two factor ANOVA data 需要是repetition data.

要回家拜託AI了 (這就是為什麼我要交錢給ChatGPT和Gemini)

W04 Chp02-The Simple Linear Regression Model

2025-10-01-Tuesday 14:00-17:00 林師模教授

• Mastering Econometrics with Joshua Angrist
• 有例題可作 簡單線性迴歸分析
• University of West Georgia Linear_regression_Notes

The Simple Linear Regression Model
Why?
simple: one dependent variable has only one independent variable.
Linear: relationship: the equation show as a line.
regression: (regress vs. progress 進步) use the already data to look back the relationship. observe the relationship of data. useing the data in the past to generate a line to look back the relationship. model: from emperical phenomeno to abstract the idea, make specification of a relationship.

例如: y: expenditure x:income
y=f(x) base on economic model
we might be able to build up a true function of the model by collecting empirical data of observation.

so we may say: y=β1 + β2 x (this is a emperical model)
true value like (xi, yi) may differenct from (xhat, yhat) which is on the regression line. so we have turn the model to: yi= β1 + β2 xi + ei (this is a econometric model) we need to use true data to estimate the β1,β2,ei parameters

yi= β1 + β2 xi + ei
y: dependent, explained被解釋, regressant, response variable
x: independet, explanatory, regressor variable
ei: erro term, residule(after we estimate model),
β1 and β2: regression coefficient, parameter
β1: intercept, constant
β2: slope (=dyi/dxi = deribative 導數 =when detax change one unit, deaty change ratio = marginal effect 邊際效應 = 當你有一個exiting situation 增加一個unit叫做 marginal unit)
這個existing situation很重要，因為可能是個critical point, 越過這個existing situation狀況可能改變，但marginal effect不隨狀況改變。
所以在這裡的modle 這個β1是個constant 和β2 是個(線性的)slope 都不會變，是個marginal effect。
注意：如果是個曲線 那麼slope 會改變，就不能算是marginal effect。
β2=dy/dx 是個marginal effect

econometric model = regression model
for every econometric model we always needs an Assumptions.
there are many Assumptions, we will look at it one by one.

今日的Quick Review:
example: 2 variable: Income=x, Expenditure=y
more income will expend more money, so there is a linear relationship. so we can set up a model:
yi= β1 + β2 xi
the distance from xi to the line we call it erro term (ei) thus come out the econometic model:
yi= β1 + β2 xi + ei
想找出β1,β2就要根據assumption 的定義
1.linear relationship
2.E(ei | xi) =0
3.Cov(xi,ei | xi) =0
4.Cov(ei,ej | xi) =0
5.xi is nonstotastic
6.ei~ N(0,δ^2)

find out the best line: estimation (estimate a value for model ): least square idea is let the total distance from data point to the line should be smallest: the sumation of all erro term shoud be minimized. in case of the summation became 0, we should square it then do the summation.
after you summation of square will became a quadratic line, then we should do firest derivative to find out the tangent line. 得出公式!!!!!!! get regression model.

老師展示example: 用Eviews:
food.wfi
先選ubcome再ctrl+foodexp open by group

Quick>estimate equation> [food_exp c income ] method: LS-least squares
OK>就可得到estimate result

W05 --本週課目標題--

2025-10-08-Tuesday 14:00-17:00 林師模教授

W06 --本週課目標題--

2025-10-15-Tuesday 14:00-17:00 林師模教授

W07 --本週課目標題--

2025-10-22-Tuesday 14:00-17:00 林師模教授

W08 --本週課目標題--

2025-10-29-Tuesday 14:00-17:00 林師模教授

W09 --本週課目標題--

2025-10-05-Tuesday 14:00-17:00 林師模教授