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# note2 - STAT5044 Regression and Anova Inyoung Kim Outline 1...

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STAT5044: Regression and Anova Inyoung Kim

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Outline 1 Regression 2 Properties of Least Squares Estimators: Gauss-Markov theorem
Regression A way to model the “relationship” between dependent ( ) variable Y and independent ( ) variable X.

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Regression A way to model the “relationship” between dependent ( ) variable Y and independent ( ) variable X. The goal of regression is to understand how the values of Y change as X is varied over its range of possible values.
Regression A way to model the “relationship” between dependent (response) variable Y and independent (explanatory) variable X. The goal of regression is to understand how the values of Y change as X is varied over its range of possible values and also predict Y using X . It is used to answer questions such as does changing class size affect success of students ? Do changes in diet result in changes in cholesterol level, and if so, do the results depend on other characteristic such as age, sex, and amount of exercise ?

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Simple Linear regression We have one response variable (Y) and one explanatory variable (X). Regression analysis was ﬁrst developed by Sir Francis Galton Galton had studied the relation between heights of father and sons Galton had noted that the heights of sons of both tall and short fathers appeared to “revert” or “regress” to the mean of the group. Galton developed a mathematical description of this regression tendency, the precursor of today’s regression models. The term regression persists to this day to describe statistical relations between variables.
Basic concepts A regression model is a formal means of expressing the two essential ingredients of a statistical relation: A tendency of the dependent variable Y to vary with the independent variable in a systematic fashion A scattering of points around the curve of statistical relationship

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Basic concepts A regression model is a formal means of expressing the two essential ingredients of a statistical relation: A tendency of the dependent variable Y to vary with the independent variable in a systematic fashion There is a probability distribution of Y for each level of X A scattering of points around the curve of statistical relationship
Basic concepts A regression model is a formal means of expressing the two essential ingredients of a statistical relation: A tendency of the dependent variable Y to vary with the independent variable in a systematic fashion There is a probability distribution of Y for each level of X A scattering of points around the curve of statistical relationship The means of these probability distributions vary in some systematic fashion with X .

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What might be of interest?
Which variables are important (when we have many X variables)?

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note2 - STAT5044 Regression and Anova Inyoung Kim Outline 1...

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