# MATHEMATICS

**12.** TABLE 13-1

A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank’s charges (*Y*)—measured in dollars per month—for services rendered to local companies. One independent variable used to predict the service charge to a company is the company’s sales revenue (*X*)—measured in millions of dollars. Data for 21 companies who use the bank’s services were used to fit the model:

*E*(*Y*) = *β*_{0} + *β*_{1}*X*

The results of the simple linear regression are provided below.

= -2,700 + 20*X*, S* _{YX}* = 65, two-tailed

*p*value = 0.034 (for testing

*β*

_{1})

Referring to Table 13-1, interpret the estimate of σ, the standard deviation of the random error term (standard error of the estimate) in the model.

[removed]A) For every $1 million increase in sales revenue, we expect a service charge to increase $65.

[removed]B) About 95% of the observed service charges equal their corresponding predicted values.

[removed]C) About 95% of the observed service charges fall within $130 of the least squares line.

[removed]D) About 95% of the observed service charges fall within $65 of the least squares line.

**13.** In a simple linear regression problem, *r* and *b*_{1}

[removed]A) must have opposite signs.

[removed]B) may have opposite signs.

[removed]C) must have the same sign.

[removed]D) are equal.

**14.** The sample correlation coefficient between *X* and *Y* is 0.375. It has been found that the *p*-value is 0.256 when testing *H*_{0} : *ρ* = 0 against the two-sided alternative *H*_{1} : *ρ* ≠ 0. To test *H*_{0} : *ρ* = 0 against the one-sided alternative *H*_{1} : *ρ* < 0 at a significance level of 0.2, the *p*-value is:

[removed]A) 0.256/2

[removed]B) 1 – 0.256/2

[removed]C) (0.256)2

[removed]D) 1 – 0.256

**15.** Assuming a linear relationship between *X* and *Y*, if the coefficient of correlation (*r*) equals – 0.30,

[removed]A) the slope (*b*_{1}) is negative.

[removed]B) variable *X* is larger than variable *Y*.

[removed]C) there is no correlation.

[removed]D) the variance of *X* is negative.

**16.** In a multiple regression model, the adjusted *r*^{2}

[removed]A) cannot be negative.

[removed]B) has to fall between 0 and +1.

[removed]C) can sometimes be greater than +1.

[removed]D) can sometimes be negative.

**17.** TABLE 14-5

A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.

SUMMARY OUTPUT

ANOVA

Referring to Table 14-5, what fraction of the variability in sales is explained by spending on capital and wages?

[removed]A) 68.9%

[removed]B) 50.9%

[removed]C) 83.0%

[removed]D) 27.0%

**18.** TABLE 14-1

A manager of a product sales group believes the number of sales made by an employee (*Y*) depends on how many years that employee has been with the company (*X*_{1}) and how he/she scored on a business aptitude test (*X*_{2}). A random sample of 8 employees provides the following:

Referring to Table 14-1, if an employee who had been with the company 5 years scored a 9 on the aptitude test, what would his estimated expected sales be?

[removed]A) 60.88

[removed]B) 79.09

[removed]C) 17.98

[removed]D) 55.62

**19.** To explain personal consumption (CONS) measured in dollars, data is collected for

A regression analysis was performed with CONS as the dependent variable and ln(CRDTLIM), ln(APR), ln(ADVT), and SEX as the independent variables. The estimated model was

= 2.28 – 0.29 ln(CRDTLIM) + 5.77 ln(APR) + 2.35 ln(ADVT) + 0.39 SEX

What is the correct interpretation for the estimated coefficient for SEX?

[removed]A) Holding everything else fixed, personal consumption for females is estimated to be 0.39% higher than males on the average.

[removed]B) Holding everything else fixed, personal consumption for males is estimated to be 0.39% higher than females on the average.

[removed]C) Holding everything else fixed, personal consumption for females is estimated to be $0.39 higher than males on the average.

[removed]D) Holding everything else fixed, personal consumption for males is estimated to be $0.39 higher than females on the average.