EXHIBIT 4 Exhibit 4 shows the multiple linear regression with (alpha) = 0.05, fo

Question

EXHIBIT 4

Exhibit 4 shows the multiple linear regression with (alpha) = 0.05, for the percentage of high school graduates who attend four-year college (college attendance rate).

1. Applying the estimated regression function, you can predict that a school district with 18 students as the average class size and 950 as the combined SAT score will have _____ of students who attend four-year college.

78%

73%

69%

67%

2. How many percent of college attendance rate’s variation can be determined by the independent variables in this regression?

38%

60%

30%

6.2%

3. For some reason, the standard error for the average class size is missing. The value of the standard error should be

unavailable unless using MS Excel calculation.

2.056.

1.007

0.993.

4. Can you confirm the estimated equation’s overall significance by F-test?

No, because the p-value
of Average Class Size is greater than 0.05.

Yes, because the p-value
of F test is less than 0.05.

Yes, because the test statistic is negative.

No, because the p-value
of F test is greater than 0.025.

5. Which of the following modifications is least likely to raise R-square in this case?

Choose another data set for a higher R square and consistent testing results.

Drop the independent variable of average class size.

Keep all variables and change the model to be exponential (log-linear) model. .

Add another independent variable such as student family income.

SUMMARY OUTPUT Regression Statistics Multiple R 0.61818055 R Square 0.38214719 Adjusted R Square 0.29976681 Standard Error 12.4169017 Observations 18 ANOVA df SS MS F Significance F Regression 2 1430.419387 715.209694 4.63881342 0.027017036 Residual 15 2312.691724 154.179448 Total 17 3743.111111 Coefficients Standard Error t Stat P-value Intercept 26.7066982 51.66892548 0.51688124 0.6127759   Average
Class Size (# of students) -1.4297536 ? -1.43972625 0.17048811 Combined
SAT Score 0.07573703 0.039055144 1.93923323 0.07151948

Explanation / Answer

1. Given Class Size X1= 18, combined SAT score X2 = 950

school distric Y = 26.7066982 -1.4297536 X1 + 0.07573703X3

=26.7066982 -1.4297536 (18) + 0.07573703(950)

= 72.92157

2. R2 = 0.38214719 = 38.215% of variations in the variable Y can be explained by the independent variables X1 and X2

Correct ansewr: option (A) 0..38 = 38%

3. SE of average class size = -1.4297536 / -1.43972625 = 0.99305

4. P-value of Regression is 0.027017036 < alpha 0.05, So we reject H0

Thus we conclude that the regression line is best fit to the given data

Correct Answer: Option (B) Yes, because the p-value of F test is less than 0.05.

5. Correct Answer: option (B) Drop the independent variable of average class size.

3.

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