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Suppose a local university researcher wants to build a linear model that predicts the freshman year...

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 0.481202. Additional sample statistics are summarized in the table below.

Variable Variable
description		 Sample
mean		 Sample standard
deviation
?x high school SAT score ?⎯⎯⎯=x¯= 1495.716802 ??=109.915203sx=109.915203
?y freshman year GPA ?⎯⎯⎯=3.260911y¯=3.260911 ??=0.492802sy=0.492802

?slope=0.481202=0.002157r=0.481202slope=0.002157

Determine the ?y‑intercept, ?a, of the least-squares regression line for this data. Give your answer precise to four decimal places. Avoid rounding until the last step.

math   Statistics-And-Probability   
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