Select all statements that are true of the least-squares regression line.) It assumes a linear relationship between the explanatory and the responsevariable.R-squared is the portion of sample variance in the explanatory variable that canbe explained by variation in the response variable.) It can be used to predict the mean response of the explanatory variable.| R-squared is the portion of sample variance in the y variable that can beexplained by variation in the x variable.

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Answered: Select all statements that are true of…

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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Which of the following is assumed for establishing the unbiassedness of Ordinary Least Square(OLS) estimates? A) The sample value outcomes on the explanatory variable are all the same value B)The error term has the same variance given any value of the explanatory variable. C)The error term has an expected value of 1 given any value of the explanatory variable D) The regression equation is linear in the explained and explanatory variables.
The y-interept bo of a least-squares regression line has a useful interpretation only if the x-values are either all positive or all negative. Determine if the statement is true or false. Why? If the statement is false, rewrite as a true statement.
The least-squares regression line relating two statistical variables is given as = 24 + 5x. Compute the residual if the actual (observed) value for y is 38 when x is 2. 4 38 2
Which of the following scatterplots provides evidence that the condition of equal variance for inference for the slope of a regression line has not been met?
(d) Determine the equation of the regression line using least squares method.(e) What is the expected breakdown for an eleven year old machine?
A manufacturer of car batteries claims that the mean lifetime of their battery is 67 months. Thinking that this claim is inflated, graduate students buy a random sample of 72 car batteries from this manufacturer. How should they proceed? a) Perform a hypothesis test of H0:μ=67 versus Ha:μ>67 b) Perform a hypothesis test of H0:μ=67 versus Ha:μ<67 c) Use Simple linear regression
(g) Compute the sum of the squared residuals for the least-squares regression line found in part (d).
Given the estimated least square regression line y=2.48+1.63x, and the coefficient of determination of 0.81, What is the value of correlation coefficient?

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