Suppose a local university researcher wants to build a linear model that predict

Question

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.

r=0.481202

Determine the slope, b, of the least squares regression line for this data. Give your answer precise to four decimal places. Avoid rounding until the last step.

b =??

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

Explanation / Answer

for lliear regression we know that slope b =r*Sy/Sx where r is correlation coefficient

=0.481202*0.492802/109.915203 =0.002157~ 0.0022

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