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. what is the value of the correlation coefficient for all 10 data points? r = 0.893 (simplify your answer. 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. 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.

Explanation:

Step1: Identify critical value for n=10

Critical value for α=0.05 and n=10 is ~0.632.

Step2: Compare r=0.893 with critical value

0.893 > 0.632, so in critical region.

Step3: Determine linear correlation for part b

Since r is in critical region, there is linear correlation.

Step4: Analyze part c (r=0)

r=0 is not in critical region (0 < 0.632 for n=9, critical value ~0.666), so no linear correlation.

Answer:

b. r=0.893; 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.