After analyzing the model, your manager has informed that your regression model is suffering from multicollinearity. How would you check if he's true? Without losing any information, can you still build a better model? Answer: To check multicollinearity, we can create a correlation matrix to identify & remove variables having correlation above 75% (deciding a threshold is subjective). In addition, we can use calculate VIF (variance inflation factor) to check the presence of multicollinearity. VIF value <= 4 suggests no multicollinearity whereas a value of >= 10 implies serious multicollinearity. Also, we can use tolerance as an indicator of multicollinearity. But, removing correlated variables might lead to loss of information. In order to retain those variables, we can use penalized regression models like ridge or lasso regression. Also, we can add some random noise in correlated variable so that the variables become different from each other. But, adding noise m...
Is rotation necessary in PCA? If yes, Why? What will happen if you don't rotate the components? Answer: Yes, rotation (orthogonal) is necessary because it maximizes the difference between variance captured by the component. This makes the components easier to interpret. Not to forget, that's the motive of doing PCA where, we aim to select fewer components (than features) which can explain the maximum variance in the data set. By doing rotation, the relative location of the components doesn't change, it only changes the actual coordinates of the points. If we don't rotate the components, the effect of PCA will diminish and we'll have to select more number of components to explain variance in the data set.
You have built a multiple regression model. Your model R² isn't as good as you wanted. For improvement, your remove the intercept term, your model R² becomes 0.8 from 0.3. Is it possible? How? Answer: Yes, it is possible. We need to understand the significance of intercept term in a regression model. The intercept term shows model prediction without any independent variable i.e. mean prediction. The formula of R² = 1 - ∑(y - y´)²/∑(y - ymean)² where y´ is predicted value. When intercept term is present, R² value evaluates your model wrt. to the mean model. In absence of intercept term (ymean), the model can make no such evaluation, with large denominator, ∑(y - y´)²/∑(y)² equation's value becomes smaller than actual, resulting in higher R².