Q43. Werner Baltz, CFA, has regressed 30 years of data to forecast future sales for National Motor Company based on the percent change in gross domestic product (GDP) and the change in price of a U.S. gallon of fuel at retail. The results are presented below. Note: results must be multiplied by $1,000,000:

In 2002, if GDP rises 2.2% and the price of fuels falls $0.15, Baltz’s model will predict Company sales in 2002 to be (in $ millions) closest to:

A)   $128.

B)   $206.

C)   $82.

Q44. Baltz proceeds to test the hypothesis that none of the independent variables has significant explanatory power. He concludes that, at a 5% level of significance:

A)   at least one of the independent variables has explanatory power, because the calculated F-statistic exceeds its critical value.

B)   none of the independent variables has explanatory power, because the calculated F-statistic does not exceed its critical value.

C)   all of the independent variables have explanatory power, because the calculated F-statistic exceeds its critical value.

Q45. Baltz then tests the individual variables, at a 5% level of significance, to determine whether sales are explained by individual changes in GDP and fuel prices. Baltz concludes that:

A)   neither GDP nor fuel price changes explain changes in sales.

B)   both GDP and fuel price changes explain changes in sales.

C)   only GDP changes explain changes in sales.

答案和详解如下：

Q43. Werner Baltz, CFA, has regressed 30 years of data to forecast future sales for National Motor Company based on the percent change in gross domestic product (GDP) and the change in price of a U.S. gallon of fuel at retail. The results are presented below. Note: results must be multiplied by $1,000,000:

In 2002, if GDP rises 2.2% and the price of fuels falls $0.15, Baltz’s model will predict Company sales in 2002 to be (in $ millions) closest to:

A)   $128.

B)   $206.

C)   $82.

Correct answer is B)

Sales will be closest to $78 + ($30.22 × 2.2) + [(−412.39) × (−$0.15)] = $206.34 million.

Q44. Baltz proceeds to test the hypothesis that none of the independent variables has significant explanatory power. He concludes that, at a 5% level of significance:

A)   at least one of the independent variables has explanatory power, because the calculated F-statistic exceeds its critical value.

B)   none of the independent variables has explanatory power, because the calculated F-statistic does not exceed its critical value.

C)   all of the independent variables have explanatory power, because the calculated F-statistic exceeds its critical value.

Correct answer is A)

From the ANOVA table, the calculated F-statistic is (mean square regression / mean square error) = 145.65 / 4.89 = 29.7853. From the F distribution table (2 df numerator, 27 df denominator) the F-critical value may be interpolated to be 3.36. Because 29.7853 is greater than 3.36, Baltz rejects the null hypothesis and concludes that at least one of the independent variables has explanatory power.

Q45. Baltz then tests the individual variables, at a 5% level of significance, to determine whether sales are explained by individual changes in GDP and fuel prices. Baltz concludes that:

A)   neither GDP nor fuel price changes explain changes in sales.

B)   both GDP and fuel price changes explain changes in sales.

C)   only GDP changes explain changes in sales.

Correct answer is B)

From the ANOVA table, the calculated t-statistics are (30.22 / 12.12) = 2.49 for GDP and (−412.39 / 183.981) = −2.24 for fuel prices. These values are both outside the t-critical value at 27 degrees of freedom of ±2.052. Therefore, Baltz is able to reject the null hypothesis that these coefficients are equal to zero, and concludes that each variable is important in explaining sales.

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