We know that the non-participating states must spend money on their pupils and then can measure their student's achievements should they choose to participate in the study. We naturally assumed that these rebel states have no academic reasons that determined whether or not they participate in the NAEP study. With that in mind, we again assume that the relationship between the variables will be very similar.
Regression Analysis: Spending Per Pupil versus Composite
(table)
We decided to conducted regression analysis despite the fact that the x value is estimated. What is interesting to note is the incredible change in value with the R-square, the F-value and the P-value. Every single one indicates an almost perfect significance. This ridiculous discrepancy may be attributed to the inaccuracy of the composite scores. For example, the reason why R-square comes out to 100% correlation, the F-value 13,667 and the P-value at 0.000 is because the x value is computed to exact proportion of the y value every single time by using the equation.