The law of diminishing marginal utility specifies the satisfaction derived from the consumption of additional units of a product. According to it, utility increases first and subsequently increases at a diminishing rate and finally decreases. A similar theory has been applied to estimate people's feelings towards the height of individuals. The author proved that people's level of satisfaction increases if their height increases at a certain level. Thereafter, it starts decreasing (data extracted from: http://ftp.iza.org/dp3344. pdf). The following equation has been derived by the author by considering height as an independent variable and subjective individual's feelings as a dependent variable. Subjective feeling of height \(=-54.28+0.67\) Actual height -0.0015 actual height squared

a. Assume the value of height starting from 100 to 400 , with 20 consecutive intervals. Construct a table for predicting the subjective feeling of people.

b. Plot the data obtained on a graph. Assuming the same dependent and independent variable, which variable would you present as legend entries?

c. Based on the graph, relate it to the definition of law of marginal utility which is introduced at the beginning of this question.

d. Based on the table calculated in (a), calculate the coefficient of multiple determination. What conclusions can you draw about the relationship between the height of individuals and the relative subjective feelings?