Walex

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. The predicted value of AUTO if PI is 4, TEEN is 0.30, and INS = 0.6 is closest to:

A) 14.90.

B) 17.50.

C) 14.10.

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Predicted AUTO [/td][td]= 10 + 1.25 (4) + 1.0 (0.30) – 2.0 (0.6)
	= 10 + 5 + 0.3 – 1.2
	= 14.10

Walex

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. The predicted value of AUTO if PI is 4, TEEN is 0.30, and INS = 0.6 is closest to:

A) 14.90.

B) 17.50.

C) 14.10.

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Predicted AUTO [/td][td]= 10 + 1.25 (4) + 1.0 (0.30) – 2.0 (0.6)
	= 10 + 5 + 0.3 – 1.2
	= 14.10

Walex

Wanda Brunner, CFA, is trying to calculate a 95% confidence interval (df = 40) for a regression equation based on the following information:

	Coefficient	Standard Error
Intercept	-10.60%	1.357
DR	0.52	0.023
CS	0.32	0.025

What are the lower and upper bounds for variable DR?

A) 0.481 to 0.559.

B) 0.474 to 0.566.

C) 0.488 to 0.552.

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The critical t-value is 2.02 at the 95% confidence level (two tailed test). The estimated slope coefficient is 0.52 and the standard error is 0.023. The 95% confidence interval is 0.52 ± (2.02)(0.023) = 0.52 ± (0.046) = 0.474 to 0.566.

Walex

Wanda Brunner, CFA, is trying to calculate a 98% confidence interval (df = 40) for a regression equation based on the following information:

	Coefficient	Standard Error
Intercept	-10.60%	1.357
DR	0.52	0.023
CS	0.32	0.025

Which of the following are closest to the lower and upper bounds for variable CS?

A) 0.267 to 0.374.

B) 0.274 to 0.367.

C) 0.260 to 0.381.

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The critical t-value is 2.42 at the 98% confidence level (two tailed test). The estimated slope coefficient is 0.32 and the standard error is 0.025. The 98% confidence interval is 0.32 ± (2.42)(0.025) = 0.32 ± (0.061) = 0.260 to 0.381.

Walex

An analyst is interested in forecasting the rate of employment growth and instability for 254 metropolitan areas around the United States. The analyst’s main purpose for these forecasts is to estimate the demand for commercial real estate in each metro area. The independent variables in the analysis represent the percentage of employment in each industry group.

Regression of Employment Growth Rates and Employment Instability on Industry Mix Variables for 254 U.S. Metro Areas
	Model 1		Model 2
Dependent Variable	Employment Growth Rate		Relative Employment Instability
Independent Variables	Coefficient Estimate	t-value	Coefficient Estimate	t-value
Intercept	–2.3913	–0.713	3.4626	0.623
% Construction Employment	0.2219	4.491	0.1715	2.096
% Manufacturing Employment	0.0136	0.393	0.0037	0.064
% Wholesale Trade Employment	–0.0092	–0.171	0.0244	0.275
% Retail Trade Employment	–0.0012	–0.031	–0.0365	–0.578
% Financial Services Employment	0.0605	1.271	–0.0344	–0.437
% Other Services Employment	0.1037	2.792	0.0208	0.338
R²	0.289		0.047
Adjusted R²	0.272		0.024
F-Statistic	16.791		2.040
Standard error of estimate	0.546		0.345

Based on the data given, which independent variables have both a statistically and an economically significant impact (at the 5% level) on metropolitan employment growth rates?

A) "% Manufacturing Employment," "% Financial Services Employment," "% Wholesale Trade Employment," and "% Retail Trade" only.

B) "% Construction Employment" and "% Other Services Employment" only.

C) "% Wholesale Trade Employment" and "% Retail Trade" only.

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The percentage of construction employment and the percentage of other services employment have a statistically significant impact on employment growth rates in U.S. metro areas. The t-statistics are 4.491 and 2.792, respectively, and the critical t is 1.96 (95% confidence and 247 degrees of freedom). In terms of economic significance, construction and other services appear to be significant. In other words, as construction employment rises 1%, the employment growth rate rises 0.2219%. The coefficients of all other variables are too close to zero to ascertain any economic significance, and their t-statistics are too low to conclude that they are statistically significant. Therefore, there are only two independent variables that are both statistically and economically significant: "% of construction employment" and "% of other services employment".
Some may argue, however, that financial services employment is also economically significant even though it is not statistically significant because of the magnitude of the coefficient. Economic significance can occur without statistical significance if there are statistical problems. For instance, the multicollinearity makes it harder to say that a variable is statistically significant. (Study Session 3, LOS 12.m)

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The coefficient standard error for the independent variable “% Construction Employment” under the relative employment instability model is closest to:

A) 0.3595.

B) 0.0818.

C) 2.2675.

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The t-statistic is computed by t-statistic = slope coefficient / coefficient standard error. Therefore, the coefficient standard error =
= slope coefficient/the t-statistic = 0.1715/2.096 = 0.0818. (Study Session 3, LOS 12.a)

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Which of the following best describes how to interpret the R2 for the employment growth rate model? Changes in the value of the:

A) independent variables cause 28.9% of the variability of the employment growth rate.

B) independent variables explain 28.9% of the variability of the employment growth rate.

C) employment growth rate explain 28.9% of the variability of the independent variables.

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The R2 indicates the percent variability of the dependent variable that is explained by the variability of the independent variables. In the employment growth rate model, the variability of the independent variables explains 28.9% of the variability of employment growth. Regression analysis does not establish a causal relationship. (Study Session 3, LOS 12.f)

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Using the following forecasts for Cedar Rapids, Iowa, the forecasted employment growth rate for that city is closest to:

Construction employment	10%
Manufacturing	30%
Wholesale trade	5%
Retail trade	20%
Financial services	15%
Other services	20%

A) 3.15%.

B) 5.54%.

C) 3.22%.

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The forecast uses the intercept and coefficient estimates for the model. The forecast is:
= −2.3913 + (0.2219)(10) + (0.0136)(30) + (−0.0092)(5) + (−0.0012)(20) + (0.0605)(15) + (0.1037)(20) = 3.15%. (Study Session 3, LOS 12.c)

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The 95% confidence interval for the coefficient estimate for “% Construction Employment” from the relative employment instability model is closest to:

A) 0.0897 to 0.2533.

B) –0.0740 to 0.4170.

C) 0.0111 to 0.3319.

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With a sample size of 254, and 254 − 6 − 1 = 247 degrees of freedom, the critical value for a two-tail 95% t-statistic is very close to the two-tail 95% statistic of 1.96. Using this critical value, the formula for the 95% confidence interval for the jth coefficient estimate is:95% confidence interval = . But first we need to figure out the coefficient standard error:

Hence, the confidence interval is 0.1715 ± 1.96(0.08182).
With 95% probability, the coefficient will range from 0.0111 to 0.3319, 95% CI = {0.0111 < b1 < 0.3319}. (Study Session 3, LOS 11.f)

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One possible problem that could jeopardize the validity of the employment growth rate model is multicollinearity. Which of the following would suggest the existence of multicollinearity?

A) The variance of the observations has increased over time.

B) There is high positive correlation between “% Manufacturing Employment,” “% Service Sector Employment,” and “% Construction Employment.”

C) The employment growth rate displays a steady upward trend during the period covered by the data.

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The problem of multicollinearity involves the existence of high correlation between two or more independent variables. Clearly, as service employment rises, construction employment must rise to facilitate the growth in these sectors. Alternatively, as manufacturing employment rises, the service sector must grow to serve the broader manufacturing sector.

• The variance of observations suggests the possible existence of heteroskedasticity.
• A steady upward trend displayed by the employment growth rate suggests the possible existence of autocorrelation.

(Study Session 3, LOS 12.j)

bapswarrior

One of the underlying assumptions of a multiple regression is that the variance of the residuals is constant for various levels of the independent variables. This quality is referred to as:

A) a linear relationship.

B) homoskedasticity.

C) a normal distribution.

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Homoskedasticity refers to the basic assumption of a multiple regression model that the variance of the error terms is constant.

bapswarrior

Which of the following statements least accurately describes one of the fundamental multiple regression assumptions?

A) The variance of the error terms is not constant (i.e., the errors are heteroskedastic).

B) The error term is normally distributed.

C) The independent variables are not random.

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The variance of the error term IS assumed to be constant, resulting in errors that are homoskedastic.

bapswarrior

Assume that in a particular multiple regression model, it is determined that the error terms are uncorrelated with each other. Which of the following statements is most accurate?

A) Unconditional heteroskedasticity present in this model should not pose a problem, but can be corrected by using robust standard errors.

B) This model is in accordance with the basic assumptions of multiple regression analysis because the errors are not serially correlated.

C) Serial correlation may be present in this multiple regression model, and can be confirmed only through a Durbin-Watson test.

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One of the basic assumptions of multiple regression analysis is that the error terms are not correlated with each other. In other words, the error terms are not serially correlated. Multicollinearity and heteroskedasticity are problems in multiple regression that are not related to the correlation of the error terms.

bapswarrior

An analyst runs a regression of monthly value-stock returns on five independent variables over 48 months. The total sum of squares is 430, and the sum of squared errors is 170. Test the null hypothesis at the 2.5% and 5% significance level that all five of the independent variables are equal to zero.

A) Rejected at 2.5% significance and 5% significance.

B) Rejected at 5% significance only.

C) Not rejected at 2.5% or 5.0% significance.

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The F-statistic is equal to the ratio of the mean squared regression (MSR) to the mean squared error (MSE).
RSS = SST – SSE = 430 – 170 = 260
MSR = 260 / 5 = 52
MSE = 170 / (48 – 5 – 1) = 4.05
F = 52 / 4.05 = 12.84
The critical F-value for 5 and 42 degrees of freedom at a 5% significance level is approximately 2.44. The critical F-value for 5 and 42 degrees of freedom at a 2.5% significance level is approximately 2.89. Therefore, we can reject the null hypothesis at either level of significance and conclude that at least one of the five independent variables explains a significant portion of the variation of the dependent variable.

bapswarrior

Consider the following analysis of variance table:

Source	Sum of Squares	Df	Mean Square
Regression	20	1	20
Error	80	20	4
Total	100	21

The F-statistic for a test of the overall significance of the model is closest to:

A) 0.20

B) 5.00

C) 0.05

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The F-statistic is equal to the ratio of the mean squared regression to the mean squared error.
F = MSR / MSE = 20 / 4 = 5.