Economics 3. (C) You have been asked by your younger sister to help her with a science fair project. Having learned regression techniques recently, you suggest that she investigate the weight-height relationship of 4th to 6th graders. Her presen- tation topic will be to explain how people at carnivals predict weight. Your model is Weight; = ,30 + lHeighi + m, where Weight is measured in pounds, and H eight4 is measured in inches above 4 feet. You collect data for roughly 100 boys and girls between the ages of nine and twelve and estimate for her the following relationship: WEEM =45.59 + 4.32Hez'ght4, R2 = 0.55. (3.81) (0.46) (a) Interpret the results in detail. And how much weight are expected if a student is 4 feet tall? You remember from the medical literature that females in the adult pop- ulation are, on average, shorter than males and weigh less. You also seem to have heard that females controlling for height, are supposed to weigh less than males. To see if this relationship holds for children, you add a binary variable (DFY) that takes on the value one for girls and is zero otherwise. Write down the model to incoporate two facts. Based on the model you wrote in (b), write down the tests for the following null hypotheses: 1. The null that both the intercepts and the slopes for boys and girls are the same: 2. The null that only the intercepts are the same for boys and girls are the same: 3. The null that only the slopes are the same for boys and girls are the same