Suppose a local university researcher wants to build a linear model that predicts the freshman year GPA of incoming students based on high school SAT scores. The researcher randomly selects a sample of 40 sophomore students at the university and gathers their freshman year GPA data and the high school SAT score reported on each of their college applications. He produces a scatterplot with SAT scores on the horizontal axis and GPA on the vertical axis. The data has a linear correlation coefficient of 0.506701. Additional sample statistics are summarized in the table below. Sample Variable Sample standard deviation mean Variable description high school SAT score freshman year GPA x= 1504.291401 sx 105.782904 у y = 3.240805 Sy = 0.441205 r=0.506701 slope = 0.002113 Determine the y-intercept, a, of the least-squares regression line for this data. Give your answer precise to at least four decimal places. a =