Question

Which conditions are required for linear regression, and do they apply to this model based on the following diagnostic plots?

a) Linearity, independence, homoscedasticity
b) Linearity, normality, homogeneity of variance
c) Independence, normality, multicollinearity
d) Linearity, homoscedasticity, multicollinearity

Answer 1

The conditions required for linear regression are linearity, independence, and homoscedasticity. These conditions are met in this model based on the given diagnostic plots.

Step-by-step explanation:

The conditions required for linear regression are a) linearity, independence, and homoscedasticity. In this model, based on the given diagnostic plots, the conditions are met. Let's break down each condition:

1. Linearity: This means that the relationship between the independent variable(s) and the dependent variable is linear. It can be checked by plotting a scatter plot, which shows whether the points follow a straight line pattern.
2. Independence: This means that the residuals (the differences between the observed and predicted values) should not be correlated with each other. It can be checked by examining the residual plot, which should show random scattering of data points.
3. Homoscedasticity: This means that the variability of the dependent variable should be constant across all levels of the independent variable(s). It can be checked by examining the residual plot, which should show similar spread (residuals) across the range of the predicted values.