Assignment 1: Basic tools

Assignment #1 Basic tools

ubmit any 4 problems out of the following:

1. Suppose the following equation describes the relationship between the average number of classes missed during a semester (missed) and the distance from school (distance, measured in miles):

missed =3 +0.5 distance.

(i)  Sketch this line, being sure to label the axes. How do you interpret the intercept in this equation?

(ii)  What is the average number of classes missed for someone who lives 4 miles away?

2.  Suppose the unemployment rate in the United States goes from 6.4% in one year to 5.6% in the next.

(i)  What is the percentage point decrease in the unemployment rate?

(ii)  By what percentage has the unemployment rate fallen?

Suppose that Person A earns \$35,000 per year and Person B earns \$42,000.

(i)  Find the exact percentage by which Person B’s salary exceeds Person A’s.

(ii)  Now, use the difference in natural logs to find the approximate percentage

difference.

4.  Suppose the following model describes the relationship between annual salary (salary)

and the number of previous years of labor market experience (exper):  log(salary) =10.6 +.027 exper.

(i)  What is salary when exper =0? When exper =5? (Hint: You will need to exponentiate.)

(ii)  Use equation (A.28) to approximate the percentage increase in salary when exper increases by five years.

(iii)  Use the results of part (i) to compute the exact percentage difference in salary when exper= 5 and exper =0. Comment on how this compares with the approximation in part (ii).

5.  Let grthemp denote the proportionate growth in employment, at the county level, from 2010 to 2015, and let salestax denote the county sales tax rate, stated as a proportion. Interpret the intercept and slope in the equation

grthemp =.039 -0.66 salestax.

6.  Suppose that in a particular state a standardized test is given to all graduating seniors. Let score denote a student’s score on the test. Someone discovers that performance on the test is related to the size of the student’s graduating high school class. The relationship is quadratic:

score= 38.1 + .082 class -.000147 class2,

where class is the number of students in the graduating class.

(i)  How do you literally interpret the value 38.1 in the equation? By itself, is it of

much interest? Explain.

(ii)  From the equation, what is the optimal size of the graduating class (the size that

maximizes the test score)? (Round your answer to the nearest integer.) What is the

highest achievable test score?

(iii)  Does it seem likely that score and class would have a deterministic relationship?

That is, is it realistic to think that once you know the size of a student’s graduating class you know, with certainty, his or her test score? Explain.

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