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 0.503202. Additional sample statistics are summarized in the table below. Variable Sample Sample standard Variable description deviation mean high school SAT score x = 1501.717708 Sx = 104.141305 y freshman year GPA y = 3.300318 Sy = 0.451901 r = 0.503202 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 =
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 0.503202. Additional sample statistics are summarized in the table below. Variable Sample Sample standard Variable description deviation mean high school SAT score x = 1501.717708 Sx = 104.141305 y freshman year GPA y = 3.300318 Sy = 0.451901 r = 0.503202 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 =
MATLAB: An Introduction with Applications
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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 0.503202. Additional sample statistics are summarized in the table below.
Variable
Sample
Sample standard
Variable
description
mean
deviation
high school SAT score
X =
x = 1501.717708
Sy =
104.141305
y
freshman year GPA
y = 3.300318
Sy
= 0.451901
r = 0.503202
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 =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0099a628-cf46-4000-ad1c-d9f2a43c0b57%2Fb248ba03-f81e-4bdc-ae4b-c12f04de9e57%2Forpzh0j_processed.png&w=3840&q=75)
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 0.503202. Additional sample statistics are summarized in the table below.
Variable
Sample
Sample standard
Variable
description
mean
deviation
high school SAT score
X =
x = 1501.717708
Sy =
104.141305
y
freshman year GPA
y = 3.300318
Sy
= 0.451901
r = 0.503202
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 =
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