Question

refer to the accompanying scatterplot. a. examine the pattern of all 10 points and subjectively determine whether there appears to be a strong correlation between x and y. b. find the value of the correlation coefficient r and determine whether there is a linear correlation. c. remove the point with coordinates (1,2) and find the correlation coefficient r and determine whether there is a linear correlation. d. what do you conclude about the possible effect from a single pair of values? click here to view a table of critical values for the correlation coefficient. b. yes, because the correlation coefficient is in the critical region. c. yes, because the correlation coefficient is not in the critical region. d. no, because the correlation coefficient is not in the critical region. c. what is the correlation coefficient when the point (1,2) is excluded? r = 0 (round to three decimal places as needed.) is there a linear correlation between x and y? use α = 0.05. a. no, because the correlation coefficient is in the critical region. b. no, because the correlation coefficient is not in the critical region. c. yes, because the correlation coefficient is in the critical region. d. yes, because the correlation coefficient is not in the critical region. d. what do you conclude about the possible effect from a single pair of values? a single pair of values does not change the conclusion. the effect from a single pair of values can change the conclusion.

Explanation:

a. From the scatterplot, most points form a tight cluster (likely no strong linear trend initially, but the outlier (1,2) affects perception).
b. The correlation coefficient r would be non-zero (with the outlier), leading to a conclusion of linear correlation if r is in the critical region.
c. Excluding (1,2), the remaining points are clustered with no linear trend, so r≈0, and there is no linear correlation.
d. Removing one point changed the correlation coefficient and the conclusion about linear correlation.

Answer:

a. (Assuming initial perception: No strong correlation, but with the outlier, it may seem weak; exact answer depends on full plot, but typical for such problems: No strong correlation)
b. B. Yes, because the correlation coefficient is in the critical region.
c. r=0; B. No, because the correlation coefficient is not in the critical region.
d. The effect from a single pair of values can change the conclusion.