1. Write out the Regression Equation 2. Interpret the coefficients for %Teachers

Question

1. Write out the Regression Equation

2. Interpret the coefficients for %Teachers and Instructional spending per pupil

3. evaluate the statistical significance of %Teachers and Instructional spending per pupil

4. Interpret Adjust R-square

5. Among the independent variables in the regression equation, which variable has the most important effect on the dependent variable (average SAT score)

6. Based on the regression results, how does bureaucracy affect student performance?

Bureaucracy and Student SAT Performance Table 2 Dependent variable = average SAT score) Independent variable Coefficient/(beta) Standard erro statistic %Central admin. %Campus admin. % Teachers -9.98 (-·061) -5.64 (-097) 1.14 (.076) 2.36 2.35 357 -4.23 -2.40 3.18 1.29 (-298) 477 (-.125) 103 005 116 -12.75 -4.66 1.83 %Block Instructional spending 0086 L051) 442 (094) % Taking Exam Constant= 860.3 R2= .20 Adi, R2 = .19 F=34.70 N of cases = 1 ,664 3.80 P .05 Note: Dummy variables used to control for autocorrelation are not reported. Coeff cient/beta column includes both unstandardized slope coefficients and betas

Explanation / Answer

1. Write out the Regression Equation

Here if average SAT score = y

so,,

y^ = 860.3 - 9.98 * (Central admin % ) - 5.64 * (Campus admin. %) + 1.14 * (%Teachers) -1.29 * (Low income) - 0.477 * (% black) + 0.0086 * (instructural spending per pupil ) + 0.442 * (% taking exam)

2. Interpret the coefficients for %Teachers and Instructional spending per pupil

Here if we increase % teachers by one percentage point then there is 1.14 unit increase in average SAT scores of students.

Similarly, if we increase one unit (dollar) in instrctional spending per pupil then that would increase 0.0086 marks in  average SAT scores of students.

3. evaluate the statistical significance of %Teachers and Instructional spending per pupil.

We will find the t and p - value to check their statistical significance.

for % teachers :

t = 3.18 ; Here as n is very high we assume tcritical =Zcritical = 1.96

so here t > 1.96 so we can say that the regression variable % teachers is significant in nature.

for Instructional spending per pupil

t = 1.83 ; Here as n is very high we assume tcritical =Zcritical = 1.96

so here t < 1.96 so we can say that the regression variable % teachers Instructional spending per pupil is not significant for the regression model.

4. Interpret Adjust R-square.

The adjusted R-squared is a modified version of R-squared that has been adjusted for the number of predictors in the model. The adjusted R-squaredincreases only if the new term improves the model more than would be expected by chance. It decreases when a predictor improves the model by less than expected by chance. Here adjusted R- square has a value of 0.19. It comapres that what is the effect of adding or subtracting a indepedent vaiable.

5. Among the independent variables in the regression equation, which variable has the most important effect on the dependent variable (average SAT score).

Here the variable which has the highest t score will have most important effect on average SAT score. So, Here the "% Low income " Factor is the most important variable which affec the independent variable.

6. Based on the regression results, how does bureaucracy affect student performance?

All bureacracy paramenters are statistically significant as their t - value is greatet than 1.96 so we could say that the bureacuracy normally effect the student performance. As the all coefficents are negative in nature that we can say that tighter bureaucracy negatively affect student performance where Central administration affects more than campus administration.

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