Question: Each year ninth-grade students in Ohio must take a proficiency test. The data (SCHOOL.xls in the CD) contains data from 47 school districts in Ohio from 1994 to 1995 school year. The variables in the data set are:

– School District: Name of school district

– Percentage Passing: Percentage of students passing the ninth-grade proficiency test

– Percentage Attendance: Daily average of the percentage of students attending class

– Salary: Average teachers salary (dollars)

– Spending: Instructional spending per pupil (dollars)

a) Set up a scatter diagram using the percentage passing the proficiency test as the dependent variable and daily attendance as the independent variable. Discuss the scatter diagram.

b) Assuming a linear relationship, find the regression coefficients, b₀, b₁, and its regression equation.

c) Interpret the meaning of the slope b₁ in this problem.

d) Find the standard error of the estimate.

e) Determine the coefficient of determination, r², and interpret its meaning.

f) Compute the coefficient of correlation r and interpret its meaning.

g) Perform a residual analysis on your results and determine the adequacy of the fit of the model.

h) At the 0.05 level of significance, is there evidence of a linear relationship between the independent variable and the dependent variable?

i) Set up a 95% confidence interval estimate of the population slope, b₁ and interpret its meaning.

j) Repeat (j)–(i) using instructional spending as the independent variable.

i) Set up a 95% confidence interval estimate of the population slope, b₁ and interpret its meaning.

k) Which of the two models is best at predicting the percentage of students who will pass the ninth-grade proficiency test? Write a short summary of your finding.