(Requires Appendix Material)At a Recent County Fair, You Observed That

question 24

Essay

(Requires Appendix material)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 slope and intercept of the regression and interpret these.
(b)Find the regression R² and explain its meaning. What other factors can you think of that might have an influence on the weight of an individual?

---

Definitions:

Gain from Sale

The profit realized from the sale of assets or investments when the selling price exceeds the original purchase price.

Operating Income

The profit earned from a firm's core business operations, excluding deductions of interest and taxes.

Operating Revenues

The income earned by a company from its normal business activities.

Operating Expenses

The costs associated with running the core operations of a business that are not directly tied to the production of goods or services, such as rent, utilities, and salaries.