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 parameter, and σi is the parameter’s standard error.  Using the information provided, the estimated intercept can be computed as b0 = t × σ0 = ?5.2 × 0.55 = ?2.86.

lianai

 

Which of the following statements is most accurate regarding the significance of the regression parameters at a 5% level of significance?

A) All of the parameter estimates are significantly different than zero at the 5% level of significance.

B) The parameter estimates for the intercept are significantly different than zero. The slope coefficients for index and size are not significant.

C) The parameter estimates for the intercept and the independent variable size are significantly different than zero. The coefficient for index is not significant.

D) None of the regression parameters are significantly different than zero at the 5% level of significance.

lianai

 

The correct answer is A

At 5% significance and 97 degrees of freedom (100 ? 3), the critical t-value is slightly greater than, but very close to, 1.984.  The t-statistic for the intercept and index are provided as ?5.2 and 2.1, respectively, and the t-statistic for size is computed as 0.6 / 0.18 = 3.33.  The absolute value of the all of the regression intercepts is greater than tcritical = 1.984.  Thus, it can be concluded that all of the parameter estimates are significantly different than zero at the 5% level of significance.

lianai

 

21、Consider the following estimated regression equation, with the standard errors of the slope coefficients as noted:

Salesi = 10.0 + 1.25 R&Di + 1.0 ADVi – 2.0 COMPi + 8.0 CAPi

where the standard error for the estimated coefficient on R&D is 0.45, the standard error for the estimated coefficient on ADV is 2.2 , the standard error for the estimated coefficient on COMP is 0.63, and the standard error for the estimated coefficient on CAP is 2.5.

The equation was estimated over 40 companies. Using a 5 percent level of significance, which of the estimated coefficients are significantly different from zero?

A) R&D, ADV, COMP, and CAP.

B) R&D, COMP, and CAP only.

C) COMP and CAP only.

D) ADV and CAP only.

lianai

 

The correct answer is B

The critical t-values for 40-4-1 = 35 degrees of freedom and a 5 percent level of significance are ± 2.03.

lianai

 

22、 Milky Way, Inc. is a large manufacturer of children’s toys and games based in the United States. Their products have high name brand recognition, and have been sold in retail outlets throughout the United States for nearly fifty years. The founding management team was bought out by a group of investors five years ago. The new management team, led by Russell Stepp, decided that Milky Way should try to expand its sales into the Western European market, which had never been tapped by the former owners. Under Stepp’s leadership, additional personnel are hired in the Research and Development department, and a new marketing plan specific to the European market is implemented. Being a new player in the European market, Stepp knows that it will take several years for Milky Way to establish its brand name in the marketplace, and is willing to make the expenditures now in exchange for increased future profitability.

Now, five years after entering the European market, Stepp is reviewing the results of his plan. Sales in Europe have slowly but steadily increased over since Milky Way’s entrance into the market, but profitability seems to have leveled out. Stepp decides to hire a consultant, Ann Hays, CFA, to review and evaluate their European strategy. One of Hays’ first tasks on the job is to perform a regression analysis on Milky Way’s European sales. She is seeking to determine whether the additional expenditures on research and development and marketing for the European market should be continued in the future.

Hays begins by establishing a relationship between the European sales of Milky Way (in millions of dollars) and the two independent variables, the number of dollars (in millions) spent on research and development (R&D) and marketing (MKTG). Based upon five years of monthly data, Hays constructs the following estimated regression equation:

Estimated Sales = 54.82 + 5.97 (MKTG) + 1.45 (R&D)

Additionally, Hays calculates the following regression estimates:

	Coefficient	Standard Error
Intercept	54.82	3.165
MKTG	5.97	1.825
R&D	1.45	0.987

Hays begins the analysis by determining if both of the independent variables are statistically significant. To test whether a coefficient is statistically significant means to test whether it is statistically significantly different from:

A)    the upper tail critical value.

B)    slope coefficient.

C)   zero.

D)   the lower tail critical value.

lianai

 

The correct answer is C

The magnitude of the coefficient reveals nothing about the importance of the independent variable in explaining the dependent variable. Therefore, it must be determined if each independent variable is statistically significant. The null hypothesis is that the slope coefficient for each independent variable equals zero.

lianai

 

The t-statistic for the marketing variable is calculated to be:

A) 3.271. 

B) 1.886. 

C) 1.469. 

D) 17.321. 

lianai

 

The correct answer is A

The t-statistic for the marketing coefficient is calculated as follows: (5.97– 0.0) / 1.825 = 3.271

Hays formulates a test structure where the decision rule is to reject the null hypothesis if the calculated test statistic is either larger than the upper tail critical value or lower than the lower tail critical value. At a 5 percent significance level with 57 degrees of freedom, assume that the two-tailed critical t-values are tc = ±2.004. Based on this information, Hays makes the following conclusions:

?            Point 1: The intercept term is statistically significant.

?            Point 2: Both independent variables contribute to explaining states for Milky Way, Inc.

?            Point 3: Both independent variables have slope coefficients that are significantly different from zero at the 5% significance level.

?            Point 4: If an F-test were being used, the null hypothesis would be rejected.

Which of Hays’ conclusions are CORRECT?

A) Points 1 and 2. 

B) Points 1 and 4. 

C) Points 2 and 3. 

D) Points 2 and 4. 

lianai

 

The correct answer is B

Hays’ Point 1 is correct. The t-statistic for the intercept term is (54.82 – 0) / 3.165 = 17.32, which is greater than the critical value of 2.004, so we can conclude that the intercept term is statistically significant.

Hays’ Points 2 and 3 are incorrect. The t-statistic for the R&D term is (1.45 – 0) / 0.987 = 1.469, which is not greater than the critical value of 2.004. This means that the R&D term does not have a slope coefficient that is greater than 0 at the 5 percent significant level. It also means that only MKTG can be said to contribute to explaining sales for Milky Way, Inc.

Hays’ Point 4 is correct. An F-test tests whether at least one of the independent variables is significantly different from zero, where the null hypothesis is that all none of the independent variables are significant. Since we know that MKTG is a significant variable (t-statistic of 3.271), we can reject the hypothesis that none of the variables are significant.