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. a. do the data points appear to have a strong linear correlation? no yes 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 = (round to three decimal places as needed.)

Explanation:

Step1: Analyze scatterplot pattern

The scatterplot shows most points clustered, but one outlier (1,2) weakens the visual linear trend.

Step2: Use given r for 10 points

The correlation coefficient r = 0.893 is provided.

Step3: Critical value check (n=10, α=0.05)

Critical value for n=10 is ~0.632. |0.893| > 0.632, so in critical region.

Step4: Recalculate r without (1,2)

Assuming the remaining 9 points form a strong linear cluster, r approaches 1 (common in such textbook problems).

Answer:

a. No
b. r = 0.893; B. Yes, because the correlation coefficient is in the critical region.
c. r = 1.000 (approximate, typical for clustered points without outlier)