Question

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.

Answer 1

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 =$(S^2x, S^2y)$  and the carariance sample = $Sxy$.  

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

$\bold{r= \frac{Sxy}{\sqrt{S^2x \times S^2 y}} }$

  $= \frac{116.25}{\sqrt{85.23} \times \sqrt{175.76}} \\\\= \frac{116.25}{ 9.23 \times 13.25}\\\\= \frac{116.25}{122.29}\\\\=0.95$