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...

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Extracted text: 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 0.501301. Additional sample statistics are summarized in the table below. Variable Sample Sample standard Variable description mean deviation high school SAT score x = 1489.712407 = 103.172601 y freshman year GPA y = 3.283911 Sy = 0.453608 r = 0.501301 slope = 0.002204 Determine the y-intercept, a, of the least-squares regression line for this data. Give your answer precise to at least four decimal places. а %—