Consider the situation where x = accelerated strength of concrete and y = 28-day cured strength. Suppose the simple linear regression model is valid for x between 1000 and 4000 and that B, = 1.25 ando = 350. Consider an experiment in which n = 7, and the x values at which observations are made are x, = 1000, x2 = 1600, xg = 1800, xg = 2700, xs = 2800, xg = 3400, and x, = 4100. A USE SALT (a) Calculate oj,, the standard deviation of B. (Round your answer to four decimal places.) oi, = (b) What is the probability that the estimated slope based on such observations will be between 1.00 and 1.50? (Round your answer to four decimal places.) (c) Suppose it is also possible to make a single observation at each of the n = 11 values x, = 2000, x, = 2100, ..., x1 = 3000. If a major objective is to estimate 6, as accurately as possible, would the experiment with n = 11 be preferable to the one with n = 7? O Yes. E(x - x)? = 1,100,000 for the n = 11 data, which is smaller than the same value for the n = 7 data. Because this value appears in the denominator of VB), the variance is larger for the choice of x values for the n = 7 data. O Yes. I(x; - x)? = 1,100,000 for the n = 11 data, which is larger than the same value for the n = 7 data. Because this value appears the denominator of V), the variance is larger for the choice of x values for the n = 7 data. O No. E(x, - x)? = 1,100,000 for the n = 11 data, which is smaller than the same value for the n = 7 data. Because this value appears in the denominator of :), the variance is smaller for the choice of x values for the n = 7 data. O No. E(x, - x)2 = 1,100,000 for the n = 11 data, which is larger than the same value for the n = 7 data. Because this value appears in the denominator of VB), the variance is larger for the choice of x values for the n = 7 data.
Consider the situation where x = accelerated strength of concrete and y = 28-day cured strength. Suppose the simple linear regression model is valid for x between 1000 and 4000 and that B, = 1.25 ando = 350. Consider an experiment in which n = 7, and the x values at which observations are made are x, = 1000, x2 = 1600, xg = 1800, xg = 2700, xs = 2800, xg = 3400, and x, = 4100. A USE SALT (a) Calculate oj,, the standard deviation of B. (Round your answer to four decimal places.) oi, = (b) What is the probability that the estimated slope based on such observations will be between 1.00 and 1.50? (Round your answer to four decimal places.) (c) Suppose it is also possible to make a single observation at each of the n = 11 values x, = 2000, x, = 2100, ..., x1 = 3000. If a major objective is to estimate 6, as accurately as possible, would the experiment with n = 11 be preferable to the one with n = 7? O Yes. E(x - x)? = 1,100,000 for the n = 11 data, which is smaller than the same value for the n = 7 data. Because this value appears in the denominator of VB), the variance is larger for the choice of x values for the n = 7 data. O Yes. I(x; - x)? = 1,100,000 for the n = 11 data, which is larger than the same value for the n = 7 data. Because this value appears the denominator of V), the variance is larger for the choice of x values for the n = 7 data. O No. E(x, - x)? = 1,100,000 for the n = 11 data, which is smaller than the same value for the n = 7 data. Because this value appears in the denominator of :), the variance is smaller for the choice of x values for the n = 7 data. O No. E(x, - x)2 = 1,100,000 for the n = 11 data, which is larger than the same value for the n = 7 data. Because this value appears in the denominator of VB), the variance is larger for the choice of x values for the n = 7 data.
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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Transcribed Image Text:Consider the situation where x = accelerated strength of concrete and y = 28-day cured strength. Suppose the simple linear regression model is valid for x between 1000 and 4000 and that 8, = 1.25 and o = 350. Consider an experiment in which n = 7,
and the x values at which observations are made are x, = 1000, x2 = 1600, x3 = 1800, x4 = 2700, x5 = 2800, xg = 3400, and x, = 4100.
A USE SALT
(a) Calculate oi,, the standard deviation of B. (Round your answer to four decimal places.)
(b) What is the probability that the estimated slope based on such observations will be between 1.00 and 1.50? (Round your answer to four decimal places.)
(c) Suppose it is also possible to make
single observation at each of the n = 11 values x, = 2000, x2 = 2100, ..., x1 = 3000. If a major objective is to estimate B, as accurately as possible, would the experiment with n = 11 be preferable to
the one with n = 7?
O Yes. E(x; - x)2 = 1,100,000 for the n = 11 data, which is smaller than the same value for the n = 7 data. Because this value appears in the denominator of VB, ), the variance is larger for the choice of x values for the n = 7 data.
O Yes. E(x; - x)2 = 1,100,000 for the n = 11 data, which is larger than the same value for the n = 7 data. Because this value appears in the denominator of VB1). the variance is larger for the choice of x values for the n = 7 data.
O No. E(x; - x) = 1,100,000 for the n = 11 data, which is smaller than the same value for the n = 7 data. Because this value appears in the denominator of VB1), the variance is smaller for the choice of x values for the n = 7 data.
O No. E(x; - x) = 1,100,000 for the n = 11 data, which is larger than the same value for the n = 7 data. Because this value appears in the denominator of VB.), the variance is larger for the choice of x values for the n = 7 data.
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