(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?

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Definitions:

Inelastic

This refers to a lack of sensitivity in the quantity demanded or supplied when the price changes.

Elastic

Describes a situation in economics where the demand or supply for a good or service significantly changes in response to a change in price.

Substitute Goods

Products or services that can be used in place of one another, with their demand being inversely related: as the price of one rises, the demand for the other increases.

Margarine

A butter substitute made from vegetable oils or animal fats, often used in cooking or as a spread.