Question

question 19 of 27 calculate and interpret the residual for the 2010 gold medal winner yu - na kim, who scored 78.50 in the short program and 150.06 in the free skate. the residual is 71.56. yu - na kims free skate score was 71.56 points higher than predicted based on her short program score. the residual is - 28.635. yu - na kims free skate score was 28.635 points lower than predicted based on her short program score. the residual is - 16.2. yu - na kims free skate score was 16.2 points lower than predicted based on her short program score. the residual is 3.765. yu - na kims free skate score was 3.765 points higher than predicted based on her short program score. the residual is - 3.765. yu - na kims free skate score was 3.765 points lower than predicted based on her short program score.

Explanation:

Step1: Recall residual formula

Residual = Observed value - Predicted value. Observed free - skate score of Yu - Na Kim is 150.06. We assume we have a regression line to predict free - skate score based on short - program score. But we are not given the prediction process, so we assume we are just comparing with the options.

Step2: Analyze each option

We check each option's residual value and its interpretation.

• Option 1: Residual = 71.56 means 150.06−Predicted value = 71.56, so Predicted value = 150.06 - 71.56=78.5 which seems not correct as per the context.
• Option 2: Residual=-28.635 means 150.06−Predicted value=-28.635, so Predicted value = 150.06 + 28.635 = 178.695 which is not likely.
• Option 3: Residual=-16.2 means 150.06−Predicted value=-16.2, so Predicted value = 150.06+16.2 = 166.26 which is also not likely.
• Option 4: Residual = 3.765 means 150.06−Predicted value = 3.765, so Predicted value = 150.06 - 3.765=146.295. This implies her free - skate score was 3.765 points higher than predicted based on her short - program score.
• Option 5: Residual=-3.765 means 150.06−Predicted value=-3.765, so Predicted value = 150.06 + 3.765 = 153.825.

Answer:

The residual is 3.765. Yu - Na Kim's free skate score was 3.765 points higher than predicted based on her short program score.