A researcher wants to estimate the relationship between years of educational attainment (✗) and the average yearly earnings of individuals (Y). For this, he collects data from a random sample of 104 individuals. From this data, he calculates the sample variances (S), S2) and the sample covariance (Sxy). If S² = 87.12, S² = 175.76, and Sxy = 118.10, then the sample correlation coefficient will be (Round your answer to two decimal places). Which of the following statements can be inferred from the value of the sample correlation coefficient calculated above? (Check all that apply.) A. The points in the scatterplot have a steep slope. B. There is a strong linear association between X and Y. C. The points in the scatterplot lie very close to a straight line. D. There is a weak linear association between X and Y. Could the researcher make general inferences about the correlation between X and Y from the sample correlation value? A. No, because the sample correlation is not an efficient estimator for the population correlation. B. No, because the sample correlation value changes from sample to sample. C. Yes, because the sample correlation is a consistent estimator for the population correlation. D. Yes, because the sample correlation is an unbiased estimator for the population correlation.
A researcher wants to estimate the relationship between years of educational attainment (✗) and the average yearly earnings of individuals (Y). For this, he collects data from a random sample of 104 individuals. From this data, he calculates the sample variances (S), S2) and the sample covariance (Sxy). If S² = 87.12, S² = 175.76, and Sxy = 118.10, then the sample correlation coefficient will be (Round your answer to two decimal places). Which of the following statements can be inferred from the value of the sample correlation coefficient calculated above? (Check all that apply.) A. The points in the scatterplot have a steep slope. B. There is a strong linear association between X and Y. C. The points in the scatterplot lie very close to a straight line. D. There is a weak linear association between X and Y. Could the researcher make general inferences about the correlation between X and Y from the sample correlation value? A. No, because the sample correlation is not an efficient estimator for the population correlation. B. No, because the sample correlation value changes from sample to sample. C. Yes, because the sample correlation is a consistent estimator for the population correlation. D. Yes, because the sample correlation is an unbiased estimator for the population correlation.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A researcher wants to estimate the relationship between years of educational attainment (✗) and the average yearly earnings of individuals (Y). For this, he collects data from a random sample of
104 individuals. From this data, he calculates the sample variances (S), S2) and the sample covariance (Sxy).
If S² = 87.12, S² = 175.76, and Sxy = 118.10, then the sample correlation coefficient will be
(Round your answer to two decimal places).
Which of the following statements can be inferred from the value of the sample correlation coefficient calculated above? (Check all that apply.)
A. The points in the scatterplot have a steep slope.
B. There is a strong linear association between X and Y.
C. The points in the scatterplot lie very close to a straight line.
D. There is a weak linear association between X and Y.
Could the researcher make general inferences about the correlation between X and Y from the sample correlation value?
A. No, because the sample correlation is not an efficient estimator for the population correlation.
B. No, because the sample correlation value changes from sample to sample.
C. Yes, because the sample correlation is a consistent estimator for the population correlation.
D. Yes, because the sample correlation is an unbiased estimator for the population correlation.
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