(Continuation from Chapter 4)At a Recent County Fair, You Observed

Essay

(Continuation from Chapter 4)At a recent county fair, you observed that at one stand people's weight was forecasted, and were surprised by the accuracy (within a range). Thinking about how the person could have predicted your weight fairly accurately (despite the fact that she did not know about your "heavy bones"), you think about how this could have been accomplished. You remember that medical charts for children contain 5%, 25%, 50%, 75% and 95% lines for a weight/height relationship and decide to conduct an experiment with 110 of your peers. You collect the data and calculate the following sums: $$\begin{array} { c } \sum _ { i = 1 } ^ { n } Y _ { i } = 17,375 , \sum _ { i = 1 } ^ { n } X _ { i } = 7,665.5 , \\\\\sum _ { i = 1 } ^ { n } y _ { i } ^ { 2 } = 94,228.8 , \sum _ { i = 1 } ^ { n } x _ { i } ^ { 2 } = 1,248.9 , \sum _ { i = 1 } ^ { n } x _ { i } y _ { i } = 7,625.9\end{array}$$ where the height is measured in inches and weight in pounds. (Small letters refer to deviations from means as in z_i = Z_i - $\bar { Z }$ )
(a)Calculate the homoskedasticity-only standard errors and, using the resulting t-statistic, perform a test on the null hypothesis that there is no relationship between height and weight in the population of college students.
(b)What is the alternative hypothesis in the above test, and what level of significance did you choose?
(c)Statistics and econometrics textbooks often ask you to calculate critical values based on some level of significance, say 1%, 5%, or 10%. What sort of criteria do you think should play a role in determining which level of significance to choose?
(d)What do you think the relationship is between testing for the significance of the slope and whether or not the regression R² is zero?