这门课程介绍一元和多元线性回归模型。 这些模型能够让你获得数据集和一个连续变量之间的关系。（比如说：）在教授的外表吸引程度和学生的评分之间有什么关联么？我们可以根据孩子母亲的特定特征来预测这个孩子的测试分数么？在这门课程当中，你将会学习线性回归的基本理论，运用免费统计软件R、RStudio分析一些数据例子来学习如何拟合、检验，以及如何利用回归模型去检验多元变量之间的关系。

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来自 Duke University 的课程

线性回归和建模

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这门课程介绍一元和多元线性回归模型。 这些模型能够让你获得数据集和一个连续变量之间的关系。（比如说：）在教授的外表吸引程度和学生的评分之间有什么关联么？我们可以根据孩子母亲的特定特征来预测这个孩子的测试分数么？在这门课程当中，你将会学习线性回归的基本理论，运用免费统计软件R、RStudio分析一些数据例子来学习如何拟合、检验，以及如何利用回归模型去检验多元变量之间的关系。

从本节课中

Multiple Regression

In this week, we’ll explore multiple regression, which allows us to model numerical response variables using multiple predictors (numerical and categorical). We will also cover inference for multiple linear regression, model selection, and model diagnostics. Hope you enjoy!

- Mine Çetinkaya-RundelAssociate Professor of the Practice

Department of Statistical Science

Welcome to the discussion on multiple linear regression.

Take a look at this data set of 1236 observations.

Where we have data from birth weight of babies

as well as a variety of variables on the baby, the birth, or the mother.

Imagine that we want to predict the birth weight of babies

from a set of these variables.

This is exactly what we mean by multiple regression.

We have a set of explanatory variables

that we use to predict a response variable.

We're going to be limiting our discussion to the case where the response variable is

numerical.

However, the explanatory variables can either be numerical or categorical.

For example in this case we have height and weight of the mother.

Those are numerical variables and whether or

not the mother smokes is that's a categorical variable.

So our response variable here is the birth weight of that baby.

And we want to try to predict that from a set of explanatory variables.

There's really no limit to how many of these you can have but

we're going to be talking about certain techniques for determining what is

a reasonable number or a reasonable set of variables to be included in the model.

We're going to start the unit with a discussion of

regression models with multiple predictors.

We're going to learn how to set up one of these models,

how to interpret the coefficient estimates,

as well as then talk about how to do inference for multiple linear regression.

We're going to talk about model selection, and

what we mean by model selection is which variable should be included versus why

should it not be included in the model.

And for that, we are going to consider things like is the variable a significant

predictor of the responsible or does it actually add something variable to

the model in terms of the predictive ability of the model.

Lastly, we're going to wrap up our discussion with model diagnostics.

These are basically the set of conditions that need to be met, for

our multiple linear regression model to be valid.

And just like with a regression with a single predictor,

we're going to talk about graphical diagnostic approaches for

determining whether the conditions for our model have been met.