SECTION 11.1 Summary

• Data for multiple linear regression consist of the values of a response variable and explanatory variables for cases. We write the data and enter them into software in the form

  	Variables
  Case			…
  1			…
  2			…
  ⋮
  			…

• Data analysis for multiple regression starts with an examination of the distribution of each of the variables and scatterplots to display the relations between the variables.

• The multiple regression equation predicts the response variable by a linear relationship with all the explanatory variables:

  The coefficients in this equation are estimated using the principle of least squares.

• The residuals for multiple linear regression are

  Always examine the distribution of the residuals and plot them against each of the explanatory variables.

  546

• The variability of the responses about the multiple regression equation is measured by the regression standard error , where is the square root of