48.4k views
0 votes
Which of the following correctly shows the general form of a multiple regression model?

1) Y = a + b1X1 + b2X2 + ... + bnXn
2) Y = a + b1X1 + b2X2 + ... + bnXn + e
3) Y = a + b1X1 + b2X2 + ... + bnXn + e1 + e2 + ... + en
4) Y = a + b1X1 + b2X2 + ... + bnXn + e1 - e2 + ... + en

User Ckhatton
by
7.2k points

1 Answer

4 votes

Final answer:

The correct general form of a multiple regression model is Y = a + b1X1 + b2X2 + ... + bnXn + e, which represents the relationship between one dependent variable and several independent variables, including an error term.

Step-by-step explanation:

The general form of a multiple regression model is depicted by the equation Y = a + b1X1 + b2X2 + ... + bnXn + e. In this equation:

  • Y is the dependent variable, or the variable we are trying to predict or explain.
  • a represents the y-intercept, which is the value of Y when all X variables are 0.
  • b1, b2, ..., bn are the regression coefficients that represent the change in the dependent variable Y for a one-unit change in the corresponding independent variable, while holding all other independent variables constant.
  • X1, X2, ..., Xn are the independent variables, or predictor variables, that we use to explain variation in Y.
  • e represents the error term, also known as the residual. This accounts for the variability in Y that cannot be explained by the linear relationship with the X variables.

Therefore, the correct choice from the provided options is: 2) Y = a + b1X1 + b2X2 + ... + bnXn + e.

User RaR
by
6.9k points