we are asked to determine the best estimate of the correlation coefficient the correlation coefficient r measures the strength and direction of a linear relationship between two variables the value is always greater than or equal to negative one and less than or equal to positive one r equals one represents a perfect positive linear correlation if r is positive as one variable increases so does the other the line of best fit will have a positive slope r equals zero represents no correlation r equals negative 1 represents a perfect negative linear correlation if r is negative as one variable increases the other decreases the line of best fit will have a negative slope let's begin by sketching a possible line of best fit for each scatter plot notice for the second scatter plot and the fourth scatter plot it's very easy to sketch a line of best fit which again is a line that best describes the behavior of the data notice how for this scatter plot if we sketch this line here it's a very good representation of the data because all the points are very close to the line of best fit which means we have a strong correlation and because the line of best fit is a negative slope or because as one variable increases the other decreases we have a very strong negative linear correlation and therefore r is going to be close to negative one so looking at the choices let's select a r equals negative 0.9 and now looking at this scattered plot here if we sketch a line to represent the behavior of this data it might look something like this and once again notice how all the points are very close to the line and therefore once again we have a very strong correlation because the line of best fit is a positive slope or because as one variable increases the other also increases we have a very strong positive linear correlation and r is very close to positive one so again looking at the choices let's select e r equals positive 0.9 now let's take a look at the remaining two scatter plots notice for the remaining scatter plots the points are more scattered so for the first scatter plot if we were to sketch a line of best fit it might look something like this notice how the slope of this line is positive and therefore r is going to be greater than one or positive but because the points are not as close to the line of best fit as they were for this line of best fit r is not going to be as close to positive one for this scatter plot as it was for this scatter plot so looking at the choices let's select d r equals positive 0.6 we still have a positive linear correlation but it's not as strong as the scatter plot here and then finally for the last scatter plot we can see in general as one variable increases the other decreases if we were to sketch a line of best fit it might look something like this so because the line of best fit is a negative slope or because as one variable increases the other decreases we know r is going to be negative or less than zero but the correlation is not as strong as it was for this scatter plot because the points are further away from the line of best fit so r is going to be negative but it's not going to be as close to negative one as this scatter plot and therefore let's select r equals negative 0.6 which is b i hope you found this helpful