# Estimating an Educational Production Function

**Paper, Order, or Assignment Requirements**

This is the SPSS analysis assignment, please make sure you are good at analyzing data through SPSS and finish all question. I’ve already finish the SPSS part of the question. I will upload all correct data output such as descriptive statistics or linear regression results for all 11 question. That means you only have to copy and paste the data that I upload for questions.

Given this set of data, you are asked to produce a report that responds to the concerns of the state government. More specifically, your supervisor is interested in recommending policies to the Superintendent of Schools that might improve reading scores for youth without substantial increases in the budget. Of particular concern are the types of resources and policies that seem to be effective as well as determining which particular resources might be substituted in production to obtain a higher impact of the present budget. Accordingly, you are asked to provide a report that presents the following information:

- What are the characteristics of the sample that we have chosen with respect to the means and variances of each of the variables? Under what conditions would you be willing to generalize the results to schools in other counties and to students at other grade levels? (How would you go about assessing the generalizability of these results to the County and the State of New Jersey as a whole?)
- Describe the distributions of the variables – do they appear to be normally distributed?
- Which variables are correlated highly with each other and why? Do you suspect collinearity might be a problem?
- Using the Coleman criterion of contribution to R² for each set of variables that are entered, first regress Reading Scores on SES (Reading Scores = a + b
_{1}SES). Then add to the model all of the school characteristics and perform a second regression (Reading Scores = b_{0}+ b_{1}SES + b_{2}T.Ed. + b_{3}T.EX.+ b_{4}T.V.S. + b_{5}L.S.) and determine the additional contribution to R² from adding the school characteristics.

Then repeat this process using the reverse order (first with only the school characteristics in the model, then adding SES in the second regression) and determine the additional contribution to R^{2} from adding SES.

What are the contributions to R² under each order of entry? How do you interpret them?

- Specify a complete regression equation using the following variables:

(Reading Scores = b_{0} + b_{1}SES + b_{2}T.Ed. + b_{3}T.EX.+ b_{4}T.V.S. + b_{5}L.S.)

Check the coefficients and the standard errors. Which coefficients do you consider to be reliable and why? What is your interpretation of each coefficient with respect to the impact of each of the variables on reading scores?

- Which variables are collinear, based upon your analysis of the regression?
- Using the residuals or unexplained portions of the reading scores from this regression equation, plot the residual against the reading score for each school. Do you observe any pattern?
- Which schools seem to be well represented by the equation, and which ones are deviants? More specifically, which schools do you consider to be “underachieving” schools and which ones are “overachievers”? How might you use this information to design a new study for attempting to assess the characteristics of underachieving and overachieving schools?
- Assume that the inputs are associated with the following prices for each additional unit:

Teacher Education $2,000 a year for each teacher with MA

Teacher Experience $500 a year for each additional year of experience

Teacher Verbal Score $200 a year for each additional point of verbal score

Library Service $10,000 a year for each additional level of services (for up to 500 students)

Assume that every school in your sample had an average of 20 teachers.

Would you wish to reallocate the budget from some inputs to other ones to improve reading scores? Which reallocations would you make, and to what extent?

- As a thought experiment, imagine that the Federal government were to give block grants to each of the states stipulating that a sum of $100,000 was to go to each school. What recommendations would you make for improving reading scores with this additional allocation?
- What recommendations would you make to the State of New Jersey for further investigation of some of the implications of this study?

***. ** Provide feedback on this exercise for improving it. What did you like about it and what did you dislike? What suggestions would you like to make for its improvement?

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