怎麼算兩列數之間的 correlatoin coefficient?
15.1 Multiple Regression Model
15.3 Coefficient of Determination
Why Adjusted?
Avoid overestimating the impact of adding an independent variable on the amount of variability explained by the estimated regression equation.
15.4 Model Assumptions
15.5 Testing for Significance
F test for overall significance; T test for individual significance
F Test
H0: β1 = β2 = … = βp = 0
Ha: One or more of the parameters is not equal to zero
n= 觀測數目
p =自變量數目
t Test
Multicollinearity 多重共線性
當多元迴歸方程總體顯著性的 F 檢驗表明有一個顯著關係時，我們可能得出單個參數沒有一個是顯著地不同於0的結論。只有當自變量之間的相關性非常小，纔有可能迴避這個問題。
F test is significant. but two t test is not significant. With x2 already in the model, x1 does not make a significant contribution to determining the value of y. 怎麼發現？當兩個自變量的 correlation coefficient >0.7
15.7 Qualitative Independent Variables
如果 qualitative variables 是兩個的話，那麼可以變成 0 1
The important point to remember is that when a qualitative variable has k levels, k-1 dummy variables are required in the multiple regression analysis.
15.8 Residual Analysis
Detecting Outliers
Minitab classifies an observation as an outlier if the value of its standardized residual is less than -2 or greater than +2.
Influential Observations
Minitab computes the leverage values and uses the rule of thumb hi > 3( p + 1)/n to identify influential observations.
Cook’s Distance
如果 Di >1，那麼表明第 i 次觀測值是一個有影響力的觀測值，並對這個觀測值做進一步的考察。
15.9 Logistic Regression
The Probability of y=1 given x1,x2,…,xp
Testing for Significance
H0: β1 = β2 = 0
Ha: One or both of the parameters is not equal to zero
G follows a chi-square distribution with degrees of freedom equal to the number of independent variables in the model
如果是一個個的 Variable，就用 z test
Managerial Use
問題是：發 coupon，想預測一下哪些消費者在收到 coupon 會用？
通過 logistics regression，得到下面的這張表：
結果：
Customers who have a Simmons credit card: Send the catalog to every customer who spent 2000 or more last year
Customers who do not have a Simmons credit card: Send the catalog to every customer who spent 6000 or more last year
Interpreting Logistic Regression Equation
The odds in favor of an event occurring is defined as the probability the event will occur divided by the probability the event will not occur.
Odds ratio: odds of a one-unit increase in only one of the independent variables.
Odds Ratio = odds1 / odds0
