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 Sx = 103.172601 y freshman year GPA y = 3.283911 Sy = 0.453608 r = 0.501301 slope = 0.002204 Determine the y-in pt, of the least-squares regression line for this data. Give your answer precise to at least four decimal places.

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 Sx = 103.172601 y freshman year GPA y = 3.283911 Sy = 0.453608 r = 0.501301 slope = 0.002204 Determine the y-in pt, of the least-squares regression line for this data. Give your answer precise to at least four decimal places.

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Description: Help please! Suppose a local university researcher wants to build a linear model that predicts the freshman year GPA of incomingstudents based on high school SAT scores. The researcher randomly selects a sample of 40 sophomore students at theuniversi

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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Help please!

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 %—

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