Economics 302Quiz #1

Professor MeyerSpring 2000

Name: ______

  1. (12 points) A director of a large employment agency wishes to study various characteristics of its job applicants. A sample of 5 applicants has been selected, and each respondent was asked about his/her previous years of work experience. The data collected is summarized in the table below:

Name / Gender / Years of work experience
Susan / Female / 4
John / Male / 3
Edward / Male / 6
Dave / Male / 0
Annie / Female / 0
  1. Find the mean years of work experience.

Mean = (4+3+6+0+0)/5 = 2.6

  1. Find the standard deviation.

Standard Deviation = =2.61

  1. What is the median years of work experience?

Median = 3

Arrange the years of experience in order from least to most and choose the middle value.

  1. (18 points) Suppose I chose one of the respondents from question 1 at random.
  2. What is the probability that the respondent is a female?

P(female) = 2/5

  1. What is the probability that the respondent has no work experience?

P(no work experience) = 2/5

  1. What is the probability that the respondent has no work experience, given that the respondent chosen is female?

P(no work experience |female) = 1/2

  1. Are the two events “no work experience” and “female” independent in my sample? Defend your answer using the definition of independent events.

No, they are not independent. For two events, A and B, to be independent, P (A | B) = P(A). If A is no work experience and B is female, this means that the probability of having no work experience (found in part b) must be equal to the probability of having no work experience given that you are female (found in part c) for the two events to be independent. Since 2/5 is not equal to 1/5, the two events are not independent.

  1. (20 points) An agent for a real estate company in a large city would like to be able to predict the monthly rental cost for apartments based on the size of the apartment as defined by square footage. A sample of 25 apartments in a particular residential neighborhood was selected. A linear regression was run with the following SAS output:

The REG Procedure

Model: MODEL1

Analysis of Variance

Sum of Mean

Source DF Squares Square F Value Pr > F

Model 1 2272289 2272289 60.25 <.0001

Error 23 867437 37715

Corrected Total 24 3139726

Root MSE 194.20265 R-Square 0.7237

Dependent Mean 1386.40000 Adj R-Sq 0.7117

Coeff Var 14.00769

Parameter Estimates

Parameter Standard

Variable Label DF Estimate Error t Value Pr > |t|

Intercept Intercept 1 176.97482 160.58062 1.10 0.2818

Size Size 1 1.06866 0.13768 7.76 <.0001

  1. Which variable would be my dependent variable? Which variable would be my independent variable?

The dependent variable is rental cost, and the independent variable is size.

  1. Write down the regression equation, as estimated by SAS.

SAS estimated the regression equation to be rent = 176.97 + 1.069*(size)

  1. Predict the average rent for an apartment that has 1000 square feet.

Average rent = 176.97 * 1.069*(1000) = 1245.63

  1. Name at least 3 other factors in addition to size might be useful in predicting monthly rent?

Other factors would include number of bedrooms, kitchen amenities, location, neighborhood, proximity to subways, noise level, etc.