Reading 12: Multiple Regression and Issues in Regression Analy 2011, interpret, center, values

土豆妮

Session 3: Quantitative Methods for Valuation
Reading 12: Multiple Regression and Issues in Regression Analysis

LOS c: Calculate and interpret 1) a confidence interval for the population value of a regression coefficient and 2) a predicted value for the dependent variable, given an estimated regression model and assumed values for the independent variables.

 

 

Consider the following estimated regression equation, with standard errors of the coefficients as indicated:

Sales_i = 10.0 + 1.25 R&D_i + 1.0 ADV_i ? 2.0 COMP_i + 8.0 CAP_i
where the standard error for R&D is 0.45, the standard error for ADV is 2.2, the standard error for COMP 0.63, and the standard error for CAP is 2.5.

Sales are in millions of dollars. An analyst is given the following predictions on the independent variables: R&D = 5, ADV = 4, COMP = 10, and CAP = 40.

The predicted level of sales is closest to:

A) $310.25 million.

B) $320.25 million.

C) $360.25 million.

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Predicted sales	= $10 + 1.25 (5) + 1.0 (4) ?2.0 (10) + 8 (40)
	= 10 + 6.25 + 4 ? 20 + 320 = $320.25

土豆妮

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

AUTO_t = 10.0 + 1.25 PI_t + 1.0 TEEN_t – 2.0 INS_t

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	= 10 + 1.25 (4) + 1.0 (0.30) – 2.0 (0.6)
	= 10 + 5 + 0.3 – 1.2
	= 14.10

土豆妮

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) 0.474 to 0.566.

B) 0.481 to 0.559.

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.

土豆妮

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) 0.260 to 0.381.

C) 0.274 to 0.367.

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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.