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 D

66,500 + 74.30(2,000) + 10,306(4) = $256,324

 

lianai

 

What percent of the variability in the dependent variable is explained by the independent variable?

A) 40.73%. 

B) 56.00%. 

C) 21.11%.

D) 12.68%. 

lianai

 

The correct answer is B

R2 = 0.56

 

lianai

 

The model indicates that at the 5% level of significance:

A) the slopes are not significant but the constant is. 

B) neither the slopes nor the constant are significant. 

C) the slopes are significant but the constant is not.

D) the slopes and the constant are statistically significant. 

lianai

 

The correct answer is C

DF = N ? k ? 1 = 32 ? 2 ? 1 = 29. The t-critical value at 5% significance for a 2-tailed test with 29 df = 2.045. T-values for the slope coefficients are 3.52 and 3.19, which are both greater than 2.045 (critical value). For the constant, the t-value of 1.2 < 2.045.

lianai

 

When a number of independent variables in a multiple regression are highly correlated with each other, the problem is called:

A) autocorrelation. 

B) homoskedasticity.

C) heteroskedasticity. 

D) multicollinearity.

lianai

 

The correct answer is D

Multicollinearity is present when the independent variables are highly correlated