Question

In order to make some money once classes are over for the semester, you’ve taken a job working for Santa at the North Pole—the pay’s not the best but you get all the candy canes and fruitcake you can eat. Santa is trying to predict which children are going to be on the naughty list versus the nice list. He has noted two correlations that seem to be informative: the correlation between a child’s parents’ behaviour (when they were children) and the child’s behaviour (r_PC) and the correlation between the child’s siblings’ behaviour and the child’s behaviour (r_SC). Santa is turning to you for statistical advice on the following questions: (a) “Ho, ho, ho. What statistic must I calculate to know how well I can predict the child’s behaviour from his or her siblings’ behaviour without an effect of the parents’ behaviour being in the mix?” (b) “Ho, ho, ho. What statistic must I calculate in order to get my best prediction of the child’s behaviour using both the parent’s behaviour and the siblings’ behaviour?”

Answer 1

a) Santa has to perform simple linear regression using response variable as child's behaviour and independent variable siblings behaviour.

He has to estimate least square regression equation .

Child's behaviour = b0 + b1*siblings behaviour

b) Santa has to perform multiple regression analysis using response variable as child's behaviour and independent variables are parent's behaviour (x1) and siblings' behaviour (x2)

He has to estimate the regression equation ,

Child's behaviour = b0 + b1*parent's behaviour + b2*siblings' behaviour