lianai

 

The correct answer is B

F = Mean Square of Regression / Mean Square of Error = 550 / 19.834 = 27.730.

 

lianai

 

2、A researcher runs a regression using 100 observations and two independent variables. The researcher will test each coefficient for being significantly different from zero. Since the sample size is large, the researcher will use the Z-values +/- 1.96 to conduct a two-tail test. The estimates of the slope coefficients B1 and B2 are 4.94 and -1.02. Their respective standard errors are 0.082 and 1.67. Which, if either, of the two hypotheses H0: B1 = 0 and H0: B2 = 0 can be rejected using the given critical Z-statistic?

A) H0: B2 = 0 but not H0: B1 = 0.

B) Neither H0: B1 = 0 and H0: B2 = 0.

C) H0: B1 = 0 but not H0: B2 = 0.

D) Both H0: B1 = 0 and H0: B2 = 0.

lianai

 

The correct answer is C

The test statistic for H0: B1 = 0 is t = 60.52 = (4.94 / 0.08), and the test statistic for H0: B2 = 0 is t = -0.61 = (-1.02 / 1.67). Since +1.96 < 60.52 and -1.96 < -0.61 < 1.96, reject H0: B1 = 0 and do not reject H0: B2 = 0.

 

lianai

 

3、A real estate agent wants to develop a model to predict the selling price of a home. The agent believes that the most important variables in determining the price of a house are its size (in square feet) and the number of bedrooms. Accordingly, he takes a random sample of 32 homes that has recently been sold. The results of the regression are:

	Coefficient	Standard Error	t-statistics
Intercept	66,500	59,292	1.12
House Size	74.30	21.11	3.52
Number of Bedrooms	10306	3230	3.19

 R² = 0.56; F = 40.73

What is the predicted price of a house that has 2,000 square feet of space and has 4 bedrooms?

A)    $114,432.

B)    $292,496.

C)   $292,496.

D)   $256,324.

lianai

 

The correct answer is C

Unconditional heteroskedasticity occurs when the heteroskedasticity is not related to the level of the independent variables. This means that it does not systematically increase or decrease with changes in the independent variable(s). Note that heteroskedasticity occurs when the variance of the residuals is different across all observations in the sample and can be detected either by examining scatter plots or using a Breusch-Pagen test.

 

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23、Consider the following estimated regression equation, with calculated t-statistics of the estimates as indicated:

AUTOt = 10.0 + 1.25 PIt + 1.0 TEENt – 2.0 INSt

with a PI calculated t-statstic of 0.45, a TEEN calculated t-statstic of 2.2, and an INS calculated t-statstic of 0.63.

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

A) PI and INS only.

B) PI, TEEN, and INS.

C) PI only.

D) TEEN only.

lianai

 

The correct answer is D

The critical t-values for 40-3-1 = 36 degrees of freedom and a 5% level of significance are ± 2.028. Therefore, only TEEN is statistically significant.

 

lianai

 

AIM 9: Define, calculate and interpret hypothesis testing for individual partial regression coefficients, joint hypothesis testing, and ANOVA.

1、Consider the following analysis of variance (ANOVA) table:

Source	Sum of squares	Degrees of freedom	Mean square
Regression	550	1	550.000
Error	750	38	19.834
Total	1,300	39

The F-statistic for the test of the fit of the model is closest to:

A)    0.965.

B)    27.730.

C)   0.423.

D)   0.733.

lianai

 

The correct answer is A

The R2 is calculated as (SST – SSE) / SST. In this example, R2 equals (389.14–146.85) / 389.14 = .623 or 62.3%. This indicates that the two independent variables together explain 62.3% of the variation in monthly sales. The value for mean squared error is not used in this calculation.

lianai

 

Stepp is concerned about the validity of Hays’ regression analysis and asks Hays if he can test for the presence of heteroskedasticity. Hays complies with Stepp’s request, and detects the presence of unconditional heteroskedasticity. Which of the following statements regarding heteroskedasticity is most correct?

A) Unconditional heteroskedasticity does create significant problems for statistical inference.

B) Heteroskedasticity occurs when the variance of the residuals in the same across all observations in the sample.

C) Unconditional heteroskedasticity usually causes no major problems with the regression.

D) Heteroskedasticity can be detected either by examining scatter plots of the residual or by using the Durbin-Watson test.