Problem 1 (22 points)

It is generally assumed that spending more money on education will lead to better prepared students. Gruber tested that assumption by collecting data for each of the 50 U.S. States. She recorded the average amount spent per pupil (Expend), the pupil/teacher ratio (PTratio), the average teacher’s salary (Salary), the percentage of students in that state taking the SAT exam (PctSAT) and the combined SAT score (SATcombined). Compute a simultaneous multiple regression on the data posted on Blackboard labeled SPSS problem 1 (choose backward entry method and interpret model 1). Use SAT combined as the dependent variable and the average amount spent per pupil (Expend), the pupil/teacher ratio (PTratio), the average teacher’s salary (Salary) and the percentage of students in that state taking the SAT exam (PctSAT) as the predictor variables. Use the output to answer the following questions.

1. (1) With all four variables in the model what percent of the variance is accounted for?
2. (1) For model 1 with all 4 predictor variables in the equation, what is the standard error of estimate?
3. (2) From the printout what numbers make the t ratio for testing the significance of PTratio?
4. (2) With all 4 variables in the model, for each unit increase in Expend what happens to Y and by how much.
5. (2) With all 4 variables in the model, for each standard deviation change in Salary how much of a standard deviation change in Y occurs and in what direction.
6. (2) Disregarding whether any of the predictor variables are significant, examine the results and tell me which predictor variable has the strongest relationship with Y and how do you know that.
7. (1) Using the simultaneous multiple regression procedure, which of the 4 predictors accounts for a significant amount of the variance in Y?
8. (1 points) What percent of the variance in Y is uniquely accounted for by PctSAT ?.
9. (1 point) The null hypothesis that is tested when using regression coefficients is what?
10. (2 points) A correlation between predictor variables of .8 or above increases the chance of colinearity problems. Which if any predictor variables are a risk for problems with collinearity?
11. (3 POINTS) Write the regression equation.
12. (1 POINT) What number from the analysis indicates the error in prediction.
13. (3 points) What is the difference between R Square and Adjusted R Square in multiple regression and why do we need to calculate both of these statistic. Be very specific and complete.
    Problem 2
    (25 points) The state of Vermont is divided into 10 health planning districts- they correspond roughly to counties. The following data represent the percentage of live births of babies weighing under 2500 grams (Y), total high-risk fertility rate for females 17 years of age or younger (X ₁ ), total high-risk fertility rate for females younger than 17 years of age or older than 35 years of age (X ₂ ), percentage of mothers with fewer than 12 years of education (X ₃ ), percentage of births to unmarried mothers (X ₄ ), and percentage of mothers not seeking medical care until the third trimester (X ₅ ).
    Calculate a multiple regression using X1 to X5 as predictors and Y as the dependent variable. using the backward procedure and interpreting the first step that is Model 1 Compute a simultaneous multiple regression on the data posted on Blackboard labeled SPSS problem 2 (choose backward entry method and interpret model 1).Use the output to answer the following questions.
14. (1) With all five variables in the model what percent of the variance is accounted for?
15. (1) For model 1 with all 5 predictor variables in the equation, what is the standard error of estimate?
16. (2) From the printout what numbers make the t ratio for testing the significance of X4?
17. (2) With all five variables in the model, for each unit increase in X1 what happens to Y and by how much.
18. (2) With all five variables in the model, for each standard deviation change in X3 how much of a standard deviation change in Y occurs and in what direction.
19. (2) Disregarding whether any of the predictor variables are significant, examine the results and tell me which predictor variable has the strongest relationship with Y and how do you know that.
20. (1) Using the simultaneous multiple regression procedure, which of the five predictors accounts for a significant amount of the variance in Y?
21. (1) What percent of the variance in Y is uniquely accounted for by X5 (that is accounted for by X5 after X1, X2, X3, X4 are accounted for).
22. (1) The null hypothesis that is tested when using regression coefficients is what?
23. (2) A correlation between predictor variables of .8 or above increases the chance of colinearity problems. Which if any predictor variables are a risk for problems with collinearity? \
24. (12 points) Explain the difference between a partial and a part correlation. (5 points)
    ____ 25. Satisfying the assumption of homoscedasticity allows you to _________.
    1. Interpret the standard error of estimate
    2. Calculate multiple R
    3. Calculate a standardized regression coefficient
    4. Decide who has been naughty or nice

Price: $27.75

Solution: The downloadable solution consists of 13 pages, 1475 words and 6 charts.
Deliverable: Word Document