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Using this table of data, we will present the following: numerical and graphical data summaries and a regression analysis to determine the relationship between the amount spent per student and the composite score on the NAEP test. We will then discuss whether the estimated regression can be applied to the data to estimate the composite scores for the 13 non-participating states. Next, we will subdivide the information by considering states that spend at least $4,000 per student, but not to exceed $6,000 and whether the relationship between the two variables produces similar results as the complete data set. Dissecting the data further, we will analyze whether we should omit the states that are spending less than $4,000 annually and more than $6,000 per student. Is the data that lies outside the majority of the test scores significant, or can it simple be viewed as possible outliers? Lastly, we want to develop estimates of the composite scores for the non-participating states and determine whether the educational achievement level of students is related to how much the state applies monies towards education. Let us begin with descriptive data and graphical analysis.
Below is a table summary of the descriptive statistics on the 35 participating states based on two variables: the spending per pupil and their composite scores. If we were to just 'eye ball' this data, we can see that for the most part, the average state spends $4985 and the average composite score is about 631.17 which is less than 50% of 1300. It is interesting to note the standard deviation of spending is at 1086 compared to the composite standard deviation of 27.58.
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