**Title: Building a Linear Model to Predict Freshman GPA Based on SAT Scores****Introduction:**A local university researcher is interested in constructing a linear model to predict the freshman year GPA of incoming students based on their high school SAT scores. The researcher selected a random sample of 40 sophomore students at the university, collecting their freshman GPA and SAT scores.**Data Summary:**The scatterplot created by the researcher plots SAT scores on the horizontal axis and GPA on the vertical axis. The data reveals a linear correlation coefficient of \( r = 0.454012 \).**Sample Statistics:**| Variable | Variable Description | Sample Mean | Sample Standard Deviation ||----------|--------------------------|-----------------|---------------------------|| \( x \) | high school SAT score | \( \bar{x} = 1503.578103 \) | \( s_x = 107.836402 \) || \( y \) | freshman year GPA | \( \bar{y} = 3.299812 \) | \( s_y = 0.517403 \) |**Task:**Determine the slope (\( b \)) of the least squares regression line for this data. Ensure to keep calculations precise up to four decimal places and avoid rounding until the final step.\[ b = \] (Provide your calculation here)This information will aid in understanding the relationship between SAT scores and academic performance during freshman year, contributing to improved academic advising and student support services.

Name: **Title: Building a Linear Model to Predict Freshman GPA Based on SAT
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Description: **Title: Building a Linear Model to Predict Freshman GPA Based on SAT Scores****Introduction:**A local university researcher is interested in constructing a linear model to predict the freshman year GPA of incoming students based on their high schoo

Solution: From the given information, r=0.454012, sx=107.836402 and sy=0.517403.Then, the slope is Thus, the slope, b, of the least squares regression line for this data is 0.0022.

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Statistics

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 0.454012. Additional sample statistics are summarized in the table below. Variable Sample Sample standard Variable description mean deviation high school SAT score x = 1503.578103 Sx = 107.836402 y freshman year GPA y = 3.299812 Sy = 0.517403 r = 0.454012 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 0.454012. Additional sample statistics are summarized in the table below. Variable Sample Sample standard Variable description mean deviation high school SAT score x = 1503.578103 Sx = 107.836402 y freshman year GPA y = 3.299812 Sy = 0.517403 r = 0.454012 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

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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