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 =

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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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
Sample
Sample standard
Variable
description
mean
deviation
high school SAT score
x = 1495.716802
Sx = 109.915203
y
freshman year GPA
y = 3.260911
Sy
0.492802
r = 0.481202
slope = 0.002157
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 =
Transcribed Image 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 0.481202. Additional sample statistics are summarized in the table below. Variable Sample Sample standard Variable description mean deviation high school SAT score x = 1495.716802 Sx = 109.915203 y freshman year GPA y = 3.260911 Sy 0.492802 r = 0.481202 slope = 0.002157 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 =
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