# MATHEMATICS

35.

In a regression analysis, a residual plot is:

A scatter diagram that plots the values of the residuals against the values of the dependent variable.

A scatter diagram that plots the values of the residuals against the values of an independent variable.

A histogram that plots the frequency of certain value ranges of the residuals.

None of the above.

36.

In a regression analysis, if a new independent variable is added and R-squared increases and adjusted R-squared decreases precipitously, what can be concluded?

The new independent variable improves the predictive power of the regression model.

The new independent variable does not improve the predictive power of the regression model.

The regression was performed incorrectly. It is impossible for R-squared to increase and adjusted R-squared decrease simultaneously.

The new independent variable’s coefficient is not significant at the 0.01 level

37.

The table below displays data the First Bank of Silverhaven (FBS) has collected on the personal savings accounts of its job-holding customers. The table includes data on the distribution of the number of accounts held by Homeowners vs. Non-Homeowners, and by whether the customer is Self-Employed or is Employed by a firm in which he or she does not have an ownership stake.

What is the probability that a given account-holder is self-employed?

15%

12%

3%

None of the above.

38.

The table below displays data the First Bank of Silverhaven (FBS) has collected on the personal savings accounts of its job-holding customers. The table includes data on the distribution of the number of accounts held by Homeowners vs. Non-Homeowners, and by whether the customer is Self-Employed or is Employed by a firm in which he or she does not have an ownership stake.

What is the conditional probability that an account-holder is employed by a firm in which he or she does not have an ownership stake, given that the account-holder is a homeowner?

82.9%

68.2%

59.5%

None of the above.

39.

The table below displays data the First Bank of Silverhaven (FBS) has collected on the personal savings accounts of its job-holding customers. The table includes data on the distribution of the number of accounts held by Homeowners vs. Non-Homeowners, and by whether the customer is Self-Employed or is Employed by a firm in which he or she does not have an ownership stake.

Which of the following statements is true?

Home ownership and employment status are statistically dependent.

The fact that a given personal account is held by a homeowner tells us nothing about the account holder’s employment status.

The fact that a given personal account is held by a self-employed person tells us nothing about the account-holder’s home ownership status.

None of the above.

40.

Electronics manufacturer SE must decide whether or not to invest in the development of a new type of battery. If the development succeeds, the market for the battery may be large or small. If it doesn’t succeed, the development efforts may or may not generate minor innovations that would offset some of the battery’s development costs. The tree below summarizes the decision.

What is the expected monetary value of developing the new battery?

$0.3 million

-$0.5 million

$0.9 million

$1.5 million

41.

Electronics manufacturer SE must decide whether or not to invest in the development of a new type of battery. If the development succeeds, the market for the battery may be large or small. If it doesn’t succeed, the development efforts may or may not generate minor innovations that would offset some of the battery’s development costs. The tree below summarizes the decision.

The EMV of developing the new battery is $300,000. Based on EMV, SE should develop the battery. If the manager chooses not to develop the battery, which of the following best describes the manager’s attitude towards this decision?

Risk averse.

Risk neutral.

Risk seeking.

Cowardly.

42.

Electronics manufacturer SE must decide whether or not to