Regression Hồi quy, tranh cãi, kỹ thuật phổ biến nhất được sử dụng trong thống kê áp dụng. Nó có thể được sử dụng với các dữ liệu được thu thập một cách rất có cấu trúc, chẳng hạn như các cuộc điều tra mẫu hoặc các thí nghiệm, nhưng nó cũng có thể được áp dụng cho dữ liệu quan sát. Exibility ° này là sức mạnh của nó nhưng cũng là điểm yếu của nó, nếu được sử dụng một cách thiếu suy nghĩ | Chapter Regression Richard Brook Off Campus Ltd. Palmerston North New Zealand Denny Meyer Massey University-Albany Palmerston North New Zealand FITTING A MODEL TO DATA What is Regression Historical Note Regression is arguably the most commonly used technique in applied statistics. It can be used with data that are collected in a very structured way such as sample surveys or experiments but it can also be applied to observational data. This flexibility is its strength but also its weakness if used in an unthinking manner. The history of the method can be traced to Sir Francis Galton who published in 1885 a paper with the title Regression toward mediocrity in hereditary stature. In essence he measured the heights of parents and found the median height of each motherfather pair and compared these medians with the height of their adult offspring. He concluded that those with very tall parents were generally taller than average but were not as tall as the median height of their parents those with short parents tended to be below average height but were not as short as the median height of their parents. Female offspring were combined with males by multiplying female heights by a factor of . Regression can be used to explain relationships or to predict outcomes. In Galton s data the median height of parents is the explanatory or predictor variable which we denote by X while the response or predicted variable is the height of the offspring denoted by Y. While the individual value of Y cannot be forecast exactly the average value can be for a given value of the explanatory variable X. Brief Overview Uppermost in the minds of the authors of this chapter is the desire to relate some basic theory to the application and practice of regression. In Sec we set out some terminology and basic theory. Section examines statistics and graphs to explore how well the regression model fits the data. Section concentrates on variables and how .
