The administrator of a school board in a large country was analyzing the average mathematics test scores in the schools under her control. She noticed that there were dramatic differences in scores among the schools. In an attempt to improve the scores of all the schools, she decided to determine the factors that account for the differences. accordingly, she tool a random sample of 40 schools across the country and, for each, determined the mean test score last year, the percentage of teachers in each school who hold at least one university degree in mathematics, the mean age, and the mean annual income (in $thousands) of mathematics teachers. Data are in file xr17-09. Use a 5% significance level.

(a) Conduct a regression analysis to develop the equation.

(b) Is the model valid?

(c) Interpret and test the coefficients.

(d) Predict with 95% confidence the test score at a school where 50% of the mathematics teachers have mathematics degrees, the mean age is 43, and the mean annual income is $48,30.