# 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, X1 = % Attendance, X2 = Salaries and X3 = 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) H1: β3 ≠ 0
[removed]B) H1: β0 ≠ 0
[removed]C) H1: β2 ≠ 0
[removed]D) H1: β1 ≠ 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, X1 = % Attendance, X2 = Salaries and X3 = 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 Cp statistic is

[removed]A) X1, X2, X3
[removed]B) X1, X3
[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 Q1 + 1.28 Q2 + 0.617 Q3

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.
Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise.
Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise.
Q3 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

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