Answer accurately all three subparts. A random sample of 22 students was selected from a class. The goal is to predict GPA (y) fromthe ACT score (x) using simple linear regression. The following data set was obtained from thesample:EX = 590,EY, = 67.871,EX,Y, = 1825.538,Ex2 = 16062,EY?= 221.0524%3DUsing the data set:a) Construct a 95% prediction interval on the average GPA of four students whose ACTscore is 28.b) Construct a 95% prediction interval for the GPA of an individual student whose ACTscore is 28.c) Construct a 95% confidence interval for the mean GPA of students whose ACT score is28.

Given information: ∑X=590,∑Y=67.871,∑X*Y=1825.538,∑X2=16062,∑Y2=221.0524n=22…

Answered: A random sample of 22 students was…

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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A researcher notes that, in a certain region, a disproportionate number of software millionaires were born around the year 1955. Is this a coincidence, or does birth year matter when gauging whether a software founder will besuccessful? The researcher investigated this question by analyzing the data shown in the accompanying table. Complete parts a through c below. a. Find the coefficient of determination for the simple linear regression model relating number (y) of software millionaire birthdays in a decade to total number (x) of births in the region. Interpret the result. The coefficient of determination is 1.___? (Round to three decimal places as needed.) This value indicates that 2.____ of the sample variation in the number of software millionaire birthdays is explained by the linear relationship with the total number of births in the region. (Round to one decimal place as needed.) b. Find the coefficient of determination for the simple linear regression model…
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