Executive compensation has risen dramatically beyond the rising levels of an average worker's wage over the years. The government is even considering a cap on high-flying salaries for executives (The New York Times, February 9 , 2009). Consider the following portion of data which links total compensation (in dollar millions) of the $455$ highest-paid CEOs in $2006$ with three measures: industry-adjusted return on assets (ROA), industry-adjusted stock return (Return) and the firm's size (Total Assets in dollar millions).

$$\begin{array}{|c|c|c|c|} \hline \text { Compensation } & \text { ROA } & \text { Return } & \text { Total Assets } \\ \hline 16.58 & 2.53 & -0.15 & 20917.5 \\ \hline 26.92 & 1.27 & 0.57 & 32659.5 \\ \hline \vdots & \vdots & \vdots & \vdots \\ \hline 2.3 & 0.45 & 0.75 & 44875.0 \\ \hline \end{array}$$

a. Estimate three simple linear regression models that use Compensation as the response variable with $\mathrm{ROA}$, Return, or Total Assets as the explanatory variable. Which model do you select? Explain.

b. Estimate multiple linear regression models that use various combinations of two, or all three, explanatory variables. Which model do you select? Explain.

When light is absorbed by an object, the radiation pressure is $P_{\text {radiation }}=I / c$. Suppose the exposed surface of an object has instead a reflective coating so that it reflects electromagnetic waves. Which of the following statements is true? Hint: Compare absorption to a completely inelastic collision and reflection to an elastic collision. (a) The force on the object due to radiation pressure is the same whether the light is absorbed or reflected. (b) The force on the object due to radiation pressure is greater by a factor of two when the light is reflected. (c) There is no force on the object due to radiation pressure when the light is reflected.

In a constant electromotive force RL circuit, we find that the current is given by $i(t)=\frac{E}{R}\left(1-e^{-R t / L}\right)+i(0) e^{-R t / L}$. Let $i (0)=0$. (a) Show that the current increases with time. (b) Find a time $t_0$ at which the current is 63 percent of E/R. This time is called the inductive time constant of the circuit. (c) Does the inductive time constant depend on i (0)? If so, in what way?

Explain how the example of agricultural fields relates species richness to stability.

Use the If S(n) is true, then S(n+1) is true form of the Inductive Step to prove the statement: Show that postage of 6 cents or more can be achieved by using only 2-cent and 7-cent stamps.

State whether each sentence is true or false. If false, replace the underlined term to make a true sentence. In mathematical induction, the assumption that a conjecture works for any particular case is called the $\underline {\text{inductive hypothesis.}}$

The demand function for a certain product is q = –300p + 10,000. The fixed expenses are $500,000 and the variable expenses are$2 per item produced. If q = 1,000 widgets, find E, the cost (expense) of producing them. Use both numbers in a complete sentence to explain what they mean.

Describe four agents of erosion. Which of these is the fastest? The slowest? Explain.

Differentiate cDNA from synthetic DNA.

Use inductive reasoning to predict the next number in each list.

$$\frac { 1 } { 2 } , \frac { 2 } { 3 } , \frac { 3 } { 4 } , \frac { 4 } { 5 } , \frac { 5 } { 6 } , \frac { 6 } { 7 } , ?$$

In the blank, identify the part of speech of the words in italics. Write $n$ for a noun and $p$ for a pronoun. Write $adj$. for an adjective and $adv$. for an adverb. Write $v$ for a verb, $prep$. for a preposition, $c$ for a conjunction, and $i$ for an interjection.
_____Others, including Yellowstone, the first national park, are located far from big cities.

Which nutrients can your body use as sources of energy?

. The issues regarding executive compensation have received extensive media attention (The New York Times, February 9, 2009). Consider a regression model that links CEO compensation (in \$millions) with the total assets of the firm (in$\ $$ millions) and the firm's industry. Dummy variables are used to represent four industries: Manufacturing Technology $d_1$, Manufacturing Other $d_2$, Financial Services $d_3$, and Nonfinancial Services $d_4$. A portion of the data for the 455 highest-paid CEOs in 2006 is shown in the accompanying table. $$ $$ \begin{array}{|c|c|c|c|c|c|} \hline \text { Compensation } & \text { Assets } & d_1 & d_2 & d_3 & d_4 \\ \hline 16.58 & 20917.5 & 1 & 0 & 0 & 0 \\ \hline 26.92 & 32659.5 & 1 & 0 & 0 & 0 \\ \hline \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ \hline 2.30 & 44875.0 & 0 & 0 & 1 & 0 \\ \hline \end{array} $$ $$ b. Interpret the estimated coefficients. $$

Take the number 153 , cube each digit, and add the cubes. What is the result? Now cube the digits of the result and add the cubes. What is the result? Use inductive reasoning to determine the result if the procedure is repeated 10 times.