In a multiple regression model with p independent variables, that is, y = β0β0 + β1β1x1x1 + ... + βpβpxpxp + ε, you have the following assumptions. Assumption 1: The error term ε is a random variable with a mean of zero; that is, E(ε) = 0 for all values of the independent variables x.
Assumption 2: The variance of ε, denoted by σ2σ2, is the same for all values of the independent variables x1x1, x2x2, ... , xpxp.
Assumption 3: The values of ε are independent.
Assumption 4: The error term ε is a normally distributed random variable.
The residuals plotted against ŷ, the predicted value of y, can be used to validate the assumptions of the multiple regression model.
The error term ε is the difference between . The residual is the difference between . The is an approximation of the , assuming that the regression model is true.
Based on the preceding residual plot, which of the following assumptions may have been violated?
Assumption 4
Assumption 2
Assumption 1
None of these choices is correct
Based on the preceding residual plot, which of the following assumptions may have been violated?
Assumption 1
Assumption 4
None of these choices is correct
Assumption 2
Based on the preceding residual plot, which of the following assumptions may have been violated?
Assumption 4
Assumption 2
Assumption 1
None of these choices is correct
Based on the preceding residual plot, which of the following assumptions may have been violated?
None of these choices is correct
Assumption 2
Assumption 1
Assumption 4
Another useful tool for validating the assumptions is a histogram of the residuals.
Based on the histogram, which of the following assumptions may have been violated?
Assumption 2
Assumption 4
Assumption 1
None of these choices is correct