# MATHEMATICS

**37.** TABLE 14-16

The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.

Following is the multiple regression output with *Y* = % *Passing* as the dependent variable, *X*_{1} = % *Attendance*, *X*_{2} = *Salaries* and *X*_{3} = *Spending*:

ANOVA

Referring to Table 14-16, which of the following is the correct alternative hypothesis to test whether instructional spending per pupil has any effect on percentage of students passing the proficiency test?

[removed]A) *H*_{1}: β_{3} ≠ 0

[removed]B) *H*_{1}: β_{0} ≠ 0

[removed]C) *H*_{1}: β_{2} ≠ 0

[removed]D) *H*_{1}: β_{1} ≠ 0

**38.** TABLE 15-5

The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (*% Passing*), daily average of the percentage of students attending class (*% Attendance*), average teacher salary in dollars (*Salaries*), and instructional spending per pupil in dollars (*Spending*) of 47 schools in the state.

Let Y = *% Passing* as the dependent variable, *X*_{1} = *% Attendance*, *X*_{2} = *Salaries* and *X*_{3} = *Spending*.

The coefficient of multiple determination (*R*) of each of the 3 predictors with all the other remaining predictors are, respectively, 0.0338, 0.4669, and 0.4743.

Following is the residual plot for % *Attendance*:

Following is the output of several multiple regression models:

Model (I):

Model (II):

Model (III):

Referring to Table 15-5, the “best” model using a 5% level of significance among those chosen by the *C _{p}* statistic is

[removed]A) *X*_{1}, *X*_{2}, *X*_{3}

[removed]B) *X*_{1}, *X*_{3}

[removed]C) either of the above

[removed]D) none of the above

**39.** TABLE 16-5

A contractor developed a multiplicative time-series model to forecast the number of contracts in future quarters, using quarterly data on number of contracts during the 3-year period from 1996 to 1998. The following is the resulting regression equation:

ln = 3.37 + 0.117 *X* – 0.083 *Q*_{1} + 1.28 *Q*_{2} + 0.617 *Q*_{3
}

where is the estimated number of contracts in a quarter

*X* is the coded quarterly value with X = 0 in the first quarter of 1996.

*Q*_{1} is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise.

*Q*_{2} is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise.

*Q*_{3} is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise.

Referring to Table 16-5, using the regression equation, which of the following values is the best forecast for the number of contracts in the third quarter of 1999?

[removed]A) 252

[removed]B) 277

[removed]C) 228

[removed]D) 311