aianjie

 

18、Henry Hilton, CFA, is undertaking an analysis of the bicycle industry.  He hypothesizes that bicycle sales (SALES) are a function of three factors: the population under 20 (POP), the level of disposable income (INCOME), and the number of dollars spent on advertising (ADV).  All data are measured in millions of units.  Hilton gathers data for the last 20 years and estimates the following equation (standard errors in parentheses): 

SALES = α + 0.004 POP + 1.031 INCOME + 2.002 ADV
(0.005)	(0.337)	(2.312)

The critical t-statistic for a 95 percent confidence level is 2.120.  Which of the independent variables is statistically different from zero at the 95 percent confidence level?

A)    INCOME and ADV.

B)    POP and ADV.

C)   INCOME only.

D)   ADV only.

aianjie

 

The correct answer is C

The calculated test statistic is coefficient/standard error. Hence, the t-stats are 0.8 for POP, 3.059 for INCOME, and 0.866 for ADV. Since the t-stat for INCOME is the only one greater than the critical t-value of 2.120, only INCOME is significantly different from zero.

 

aianjie

 

19、Henry Hilton, CFA, is undertaking an analysis of the bicycle industry.  He hypothesizes that bicycle sales (SALES) are a function of three factors: the population under 20 (POP), the level of disposable income (INCOME), and the number of dollars spent on advertising (ADV).  All data are measured in millions of units.  Hilton gathers data for the last 20 years and estimates the following equation (standard errors in parentheses):

SALES = 0.000  +  0.004 POP + 1.031 INCOME + 2.002 ADV
(0.113)	(0.005)	(0.337)	(2.312)

For next year, Hilton estimates the following parameters: (1) the population under 20 will be 120 million, (2) disposable income will be $300,000,000, and (3) advertising expenditures will be $100,000,000.  Based on these estimates and the regression equation, what are predicted sales for the industry for next year?

A)    $557,143,000.

B)    $509,980,000.

C)   $656,991,000.

D)   $669,471,000.

aianjie

 

The correct answer is B

Predicted sales for next year are:

SALES = α + 0.004 (120) + 1.031 (300) + 2.002 (100) = 509,980,000.

 

aianjie

 

20、Consider a study of 100 university endowment funds that was conducted to determine if the funds’ annual risk-adjusted returns could be explained by the size of the fund and the percentage of fund assets that are managed to an indexing strategy. The equation used to model this relationship is:

ARAR_i = b₀ + b₁Size_i + b₂Index_i + e_i

Where:

ARARi	=	the average annual risk-adjusted percent returns for the fund i over the 1998-2002 time period.
Sizei	=	the natural logarithm of the average assets under management for fund i.
Indexi	=	the percentage of assets in fund i that were managed to an indexing strategy.

The table below contains a portion of the regression results from the study.

Partial Results from Regression ARAR on Size and Extent of Indexing
	Coefficients	Standard Error	t-Statistic
Intercept	???	0.55	?5.2
Size	0.6	0.18	???
Index	1.1	???	2.1

Which of the following is the most accurate interpretation of the slope coefficient for size? ARAR:

A)    will change by 1.0% when the natural logarithm of assets under management changes by 0.6, holding index constant.

B)    will change by 0.6% when the natural logarithm of assets under management changes by 1.0, holding index constant.

C)   and index will change by 1.1% when the natural logarithm of assets under management changes by 1.0.

D)   will change by 1.1% when the natural logarithm of assets under management changes by 1.0 and index changes by 0.6.

aianjie

 

The correct answer is B

A slope coefficient in a multiple linear regression model measures how much the dependent variable changes for a one-unit change in the independent variable, holding all other independent variables constant. In this case, the independent variable size (= ln average assets under management) has a slope coefficient of 0.6, indicating that the dependent variable ARAR will change by 0.6% return for a one-unit change in size, assuming nothing else changes. Pay attention to the units on the dependent variable.

Which of the following is the estimated standard error of the regression coefficient for index?

A) 1.91.

B) 2.31.

C) 0.52.

D) 1.00.

aianjie

 

The correct answer is C

The t-statistic for testing the null hypothesis H0:  βi = 0 is t = (bi ? 0) / σi, where βi is the population parameter for independent variable i, bi is the estimated coefficient, and σi is the coefficient standard error.  Using the information provided, the estimated coefficient standard error can be computed as bIndex / t = σIndex = 1.1 / 2.1 = 0.5238.

aianjie

 

Which of the following is the t-statistic for size?

A) 0.30.

B) ?0.12.

C) 0.70.

D) 3.33.

aianjie

 

The correct answer is D

The t-statistic for testing the null hypothesis H0:  βi = 0 is t = (bi ? 0) / σi, where βi is the population parameter for independent variable i, bi is the estimated coefficient, and σi is the coefficient standard error.  Using the information provided, the t-statistic for size can be computed as t = bSize / σSize = 0.6 / 0.18 = 3.3333.

aianjie

 

Which of the following is the estimated intercept for the regression?

A) ?0.11.

B) ?9.45.

C) ?2.86.

D) ?4.65.