Budget and Box Office 3 000 Avatar 1500 Avatar 2 500 . Titanic 1000 2 000 Titani

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Budget and Box Office 3 000 Avatar 1500 Avatar 2 500 . Titanic 1000 2 000 Titanic 1500 500 Residual 1000 ys 2.8 1+682.453 500 500 $150 Budget (M) S0 $50 $100 200 $250 $300 1000 500 1500 Fitted Values of Box Office Consider the above scatter diagram and the residual-fitted values plot for 24 of the top grossing movies of all time. The data include the highest grossing films for which world box office receipts and budgets were available. The top two were Avatar and Titanic. The best practice for modelling this data set given the scatter plot would be

Explanation / Answer

Ans. Last option(option 4)

Here the two observations Titanic and avatar are Influencial observations as well as an outlier:

An influential observation is an observation for a statistical calculation whose deletion from the dataset would noticeably change the result of the calculation. In particular, in regression analysis an influential point is one whose deletion has a large effect on the parameter estimates.

An outlier is a data point whose response y does not follow the general trend of the rest of the data.

A data point has high leverage if it has "extreme" predictor x values. With a single predictor, an extreme x value is simply one that is particularly high or low. With multiple predictors, extreme x values may be particularly high or low for one or more predictors, or may be "unusual" combinations of predictor values (e.g., with two predictors that are positively correlated, an unusual combination of predictor values might be a high value of one predictor paired with a low value of the other predictor).

In short, If the predicted responses, estimated slope coefficients, and hypothesis test results are not affected by the inclusion of the data point , then the data point is not deemed influential. So, The best strategy is to calculate the regression lines in both cases(including and excluding the points), and to see how they differ.

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