When λ = 0, this penalty term has no effect and lasso regression produces the same coefficient estimates as least squares. This second term in the equation is known as a shrinkage penalty. One way to get around this issue is to use a method known as lasso regression, which instead seeks to minimize the following: That is, when the model is applied to a new set of data it hasn’t seen before, it’s likely to perform poorly. This can cause the coefficient estimates of the model to be unreliable and have high variance. However, when the predictor variables are highly correlated then multicollinearity can become a problem. ŷ i: The predicted response value based on the multiple linear regression model.y i: The actual response value for the i th observation.The values for β 0, β 1, B 2, …, β p are chosen using the least square method, which minimizes the sum of squared residuals (RSS): β j: The average effect on Y of a one unit increase in X j, holding all other predictors fixed.

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Hedonic regression