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A student wants to study whether there is any relationship between the amount of calories (C) consumed by the cattle and their weight (Y). He selects a random sample of 150 cattle and asks their caretakers about their calorie intake. Consider the following regression function: + uj, :- = Po +P, G, + v, where v; = B1 (C; - C;) + u; and Bo and ß, denote the intercept and the slope coefficient on C;, respectively. The population regression equation written in terms of C; has an error term that contains the measurement error, the difference between C; and C;. Suppose the student discovers that the measured value, C;, equals the actual, unmeasured value, C¡, plus a purely random component, w;. Suppose the variance of C; (o) and the variance of w; (o) are 0.09 and 0.04, respectively. Then, under the classical measurement error model, as the sample size increases, the value to which the slope estimator will converge to is B1. (Round your answer to two decimal places.)

A student wants to study whether there is any relationship between the amount of calories (C) consumed by the cattle and their weight (Y). He selects a random sample of 150 cattle and asks their caretakers about their calorie intake. Consider the following regression function: + uj, :- = Po +P, G, + v, where v; = B1 (C; - C;) + u; and Bo and ß, denote the intercept and the slope coefficient on C;, respectively. The population regression equation written in terms of C; has an error term that contains the measurement error, the difference between C; and C;. Suppose the student discovers that the measured value, C;, equals the actual, unmeasured value, C¡, plus a purely random component, w;. Suppose the variance of C; (o) and the variance of w; (o) are 0.09 and 0.04, respectively. Then, under the classical measurement error model, as the sample size increases, the value to which the slope estimator will converge to is B1. (Round your answer to two decimal places.)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 8E
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A student wants to study whether there is any relationship between the amount of calories (C) consumed by the cattle and their weight (Y). He selects a random sample of 150 cattle and asks their caretakers about their calorie intake. Consider the following regression function: Y; = Po +B, C; + B, (c, + Uj, - + = Bo + B, C, + v, where v; = B1 C; +u; and Bo and B, denote the intercept and the slope coefficient on C;, respectively. - The population regression equation written in terms of C; has an error term that contains the measurement error, the difference between C; and C;. Suppose the student discovers that the measured value, C;, equals the actual, unmeasured value, C;, plus a purely random component, W;. Suppose the variance of C; (o) and the variance of w; (om) are 0.09 and 0.04, respectively. Then, under the classical measurement error model, as the sample size increases, the value to which the slope estimator will converge to is B1. (Round your answer to two decimal places.)
Transcribed Image Text:A student wants to study whether there is any relationship between the amount of calories (C) consumed by the cattle and their weight (Y). He selects a random sample of 150 cattle and asks their caretakers about their calorie intake. Consider the following regression function: Y; = Po +B, C; + B, (c, + Uj, - + = Bo + B, C, + v, where v; = B1 C; +u; and Bo and B, denote the intercept and the slope coefficient on C;, respectively. - The population regression equation written in terms of C; has an error term that contains the measurement error, the difference between C; and C;. Suppose the student discovers that the measured value, C;, equals the actual, unmeasured value, C;, plus a purely random component, W;. Suppose the variance of C; (o) and the variance of w; (om) are 0.09 and 0.04, respectively. Then, under the classical measurement error model, as the sample size increases, the value to which the slope estimator will converge to is B1. (Round your answer to two decimal places.)
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