Clusters Refer to the Minitab-generated scatterplot. The four ...

Question

Clusters Refer to the Minitab-generated scatterplot. The four points in the lower left corner are measurements from women, and the four points in the upper right corner are from men.

Scatterplot showing four points in the lower left corner representing women's measurements and four in the upper right for men.

a. Examine the pattern of the four points in the lower left corner (from women) only, and subjectively determine whether there appears to be a correlation between x and y for women.

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Refer to the scatter plot given below. Examine the pattern of the points in the lower left cluster only based on their positions, subjectively determine whether there appears to be a positive, negative, or no correlation between that clusters of X and Y values. Awesome. So it appears for this particular problem, we're ultimately trying to figure out, focusing our attention only on the left hand cluster of our scatter plot dots only. We're trying to determine whether or not there appears to be a positive, negative, or no correlation between the clusters of X and Y values. So looking quickly at our scatter plot that is provided to us, we have two clusters of data. So on our upper right-hand corner, we're gonna ignore that cluster of dots in our upper right-hand corner, which I'll circle in blue. We're going to be ignoring. This cluster of data, and we're gonna be focusing our attention rather on the left-hand corner, which I'll circle in green. So we're focusing only on these 4 coordinate points versus the 5 coordinate points that are in the upper right, because we're asked to focus just on the left. Awesome. So with that said, let's take a moment here to read off our multiple choice answers to see what our final answer might be. A is positive correlation, B is negative correlation, and C is no correlation. Awesome. So, first off, in order to solve this particular problem, we need to observe the pattern. So we need to note and recall that the X values are either 1 or 2, so there are only 2 distinct X values, so 2, and I'll say D for distinct values, so only 2 distinct X values. Also, so there's only two distinct X values. The Y values, as we should note and recall in from this particular prompt, do not show a clear, increasing or decreasing trend when moving from one X value to another, and for X is equal to 1, we will have Y is equal to 1. And Y is equal to 3, which does show variation, and for when X is equal to 2, we will have Y is equal to 2 and Y will be equal to 3, which again will show variation. So we know now that they both show variation for X equals 1 and X equals 2 for Y equals 1 and Y equals 3 and Y equals 2 and Y equals 3. So now, our second step is we now need to determine the correlation. So with that said, we need to note and recall that since the Y values vary for the same X value, for example, X equals 1 has both Y equals 1 and Y equals 3. And similarly, for X equals 2, there is no clear linear relationship between X and Y, so that will mean in conclusion that there is no significant correlation between X and Y for the lower left cluster, because the points do not follow a clear positive or negative trend. So that will mean that our final answer, without a doubt has to be multiple choice answer letter C, which once again letter C states no correlation. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Scatterplot

Correlation

Subjective Analysis

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