Final answer:
a) Top left: Low rebounds, high free throw percentage; Bottom right: High rebounds, low free throw percentage.
b) Direction can't be determined without the scatterplot.
c) Best guess at correlation depends on scatterplot trend.
d) Impossible values: 20 and -2; Correlation is between -1 and 1.
Step-by-step explanation:
It seems like the scatterplot description is missing, but I can still provide some general guidance based on the questions you've asked.
a) The top left of a scatterplot typically represents data points with a low value on the x-axis (rebound) and a high value on the y-axis (free throw percentage).
This could suggest a player who doesn't get many rebounds but has a high free throw percentage.
Conversely, the bottom right of the scatterplot usually represents data points with a high value on the x-axis (rebound) and a low value on the y-axis (free throw percentage).
This might indicate a player who gets a lot of rebounds but has a lower free throw percentage.
b) The direction of association is determined by whether the points on the scatterplot tend to move from the bottom left to the top right (positive association) or from the top left to the bottom right (negative association).
If the free throw percentage tends to increase as the number of rebounds increases, it's a positive association. If it decreases, it's a negative association.
c) Without the scatterplot, it's challenging to precisely determine the correlation, but based on the general description:
If the points are in a perfect straight line increasing from bottom left to top right, the correlation is 1.
If they are in a perfect straight line decreasing from top left to bottom right, the correlation is -1.
If there's no apparent pattern, the correlation is 0.
Select the value that best represents the trend in your scatterplot.
d) The correlation coefficient is a value between -1 and 1. So, the values 20 and -2 are impossible for correlation coefficients. Correlation coefficients outside the range of -1 to 1 don't make sense in the context of linear relationships between variables.
The correlation cannot be stronger than a perfect positive correlation (1) or a perfect negative correlation (-1).
Your correct question is: This scatterplot below is representing the relationship between the free throw percentage and the number of rebounds in a season, for players of the National Basketball Association. 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0 200 400 1200 600 Rebounds 800 1000 a) What can we say about a player represented in the top left of the scatterplot and in the bottom right of the scatterplot? b) Is the direction of association appearing to be more positive or negative? What does that mean in this context? c) Which value is the best guess at the correlation (circle one) 20 -2, 1, -0.9, -0.4, 0, 0.4, 0.9,1, 2, 20 d) Which of the values listed in part (e) are impossible values for a correlation? Explain why?