Section 14.1 Student Learning Objectives
In the previous chapter we examined the situation where the response is numeric and the explanatory variable is a factor with two levels. This chapter deals with the case where both the response and the explanatory variables are numeric. The method that is used in order to describe the relations between the two variables is regression. Here we apply linear regression to deal with a linear relation between two numeric variables. This type of regression fits a line to the data. The line summarizes the effect of the explanatory variable on the distribution of the response.
Statistical inference can be conducted in the context of regression. Specifically, one may fit the regression model to the data. This corresponds to the point estimation of the parameters of the model. Also, one may produce confidence intervals for the parameters and carry out hypotheses testing. Another issue that is considered is the assessment of the percentage of variability of the response that is explained by the regression model.
By the end of this chapter, the student should be able to:
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Produce scatter plots of the response and the explanatory variable.
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Explain the relation between a line and the parameters of a linear equation. Add lines to a scatter plot.
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Fit the linear regression to data using the function “
lm” and conduct statistical inference on the fitted model. -
Explain the relations among \(R^2\text{,}\) the percentage of response variability explained by the regression model, the variability of the regression residuals, and the variance of the response.
