A researcher wants to estimate the relationship between years of educational attainment (X) and the average yearly earnings of individuals (Y). For this, he collects data from a random sample of individuals. From this data, he calculates the sample variances (, ) and the sample covariance (). If , , and , then the sample correlation coefficient will be nothing. (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. There is a weak linear association between X and Y. 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. The points in the scatterplot have a steep slope. Could the researcher make general inferences about the correlation between X and Y from the sample correlation value? A. Yes, because the sample correlation is a consistent estimator for the population correlation. B. No, because the sample correlation is not an efficient estimator for the population correlation. C. Yes, because the sample correlation is an unbiased estimator for the population correlation. D. No, because the sample correlation value changes from sample to sample.

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codiepienagoya codiepienagoya · Answer 1 · 2020-10-06T06:51:30+02:00

Answer:

The answer is "Option a and Option b".

Step-by-step explanation:

In the given question, the data value is missing which is defined in the attached file, please find it.

We have variance sample =[tex](S^2x, S^2y)[/tex] and the carariance sample = [tex]Sxy[/tex].

if "[tex]S^2x = 85.27, S^2y = 175.76, and \ \ Sxy = 116.25[/tex]" its sample coefficient correlation will be defined as follows:

[tex]\bold{r= \frac{Sxy}{\sqrt{S^2x \times S^2 y}} }\\\\[/tex]

[tex]= \frac{116.25}{\sqrt{85.23} \times \sqrt{175.76}} \\\\= \frac{116.25}{ 9.23 \times 13.25}\\\\= \frac{116.25}{122.29}\\\\=0.95[/tex]