Here are plots of the residuals for a multiple linear regression model. Why is t

Question

Here are plots of the residuals for a multiple linear regression model. Why is this a bad model?

a.) There is no relationship between the variables at all, the r^2 value should be 0.

b.) We have a problem with non-constant variance, We should try the model again but this time with log(response).

c.) Our errors are not normally distributed, we should consider a model with perhaps more predictors to remove more of the trend

d.) Our errors do not consistently have mean = 0. We should probably consider a transformation of our predictors and/or additional predictors to better fit the response.

Please a brief explanation for your answer.

Explanation / Answer

Answer:

Here are plots of the residuals for a multiple linear regression model. Why

a.) There is no relationship between the variables at all, the r^2 value should be 0.

b.) We have a problem with non-constant variance, We should try the model again but this time with log(response).

c.) Our errors are not normally distributed, we should consider a model with perhaps more predictors to remove more of the trend

d.) Our errors do not consistently have mean = 0. We should probably consider a transformation of our predictors and/or additional predictors to better fit the response. - Correct Answer

Explanation: Based on the residual vs fitted plot there is a noticable pattern (non linearity) in the residual (error terms). When the fitted values are large or small the error term is positive and in the middle of the curve the error terms are negative. Therefore the errors are not scattered randomly across the 0 line and may not be independent. In this case it is recommended to transform the predictor variables to better fit the response.

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