Outlier Refer to the accompanying Minitab-generated scatterplo...

Question

Outlier Refer to the accompanying Minitab-generated scatterplot.

Scatterplot showing 10 data points with one outlier above the main cluster of points. Axes labeled X and Y.

b. After identifying the 10 pairs of coordinates corresponding to the 10 points, find the value of the correlation coefficient r and determine whether there is a linear correlation.

Accepted Answer

Below 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. After identifying the 10 data points represented in the scatter plot, calculate the correlation coefficient R based on the value of R, determine whether there is a linear correlation between the two variables. Awesome. So it appears for this particular problem we're asked to solve for two separate answers. So our first answer is we're trying to figure out ultimately what the value of the correlation coefficient is. So we're trying to figure out what the value of R is. That's our first answer we're trying to solve for. Secondly, based on what value we determine for R, we need to determine whether or not there is a linear correlation between the two variables, and that is our second answer we're ultimately trying to solve for. And as you can see, referring to the scatter plot that is provided to us, we have several dots that are lined up together that that form the shape of a square, and it appears there are 12345678. 9. There's 9 coordinate dots that form a square in the bottom left hand corner of our XY coordinate plane, and then we have 1 singular data point way up above which appears to be at 9.10. Awesome. So now that we have a visualization of what's happening for this particular prompt, let's take a moment to read off our multiple choice answers to see what our final answer pair might be, noting that our first answer states that R is equal to some value. So A is 0, and there is no significant linear correlation between the two variables. B is 0.88, and there is a strong positive linear correlation. C is 0.12 and there is a weak linear correlation and finally D is negative 0.88, and there is a strong negative correlation between the two variables. Awesome. So with that said, our first step that we need to take in order to solve this particular problem is we need to First off, we need to write down, or rather identify the 10 pairs of points. Since we said that we have the 9 points that form like a square shape on our graph, and then we have 1 other coordinate point floating off on its own. So with that said, we need to write down our 10 pairs of points. So our first pair is 1.2, then we have 1.3, then we have 1.4, once again, these are all in parentheses. Then we have 2.2. Then we have 2.3. Then we have 2.4. Then we have 3.2. Then we have 3.3. Then we have 3.4, and then finally we have 9.10. Fantastic. So now, our next step is we need to recall and use the Pearson correlation coefficient R equation. So we need to recall and use our equation to solve for R, which is the correlation coefficient, and as we should recall, R should be equal to N multiplied by sigma. So once again it's gonna be N multiplied by sigma. Multiplied by X, multiplied by Y minus parenthesis. Sigma multiplied by X, multiplied by parenthesis. Sigma multiplied by Y. All divided by the square root of N multiplied by sigma, multiplied by X2. Minus parenthesis. Sigma Multiplied by X2. Fantastic. And it's more specifically, it's sigma multiplied by X and then sigma multiplied by X is the power of 2, that's very important to note, multiplied by the square root of N multiplied by Sigma multiplied by Y2 minus parenthesis sigma multiplied by Y to the power of 2. So it's gonna be sigma multiplied by Y to the power 2. Fantastic. So, our next step now is we need to create a table to help us combine our calculations. So we could tabulate our calculations as the following. So I've gone ahead and created a table for us to refer to. And as you can see, going along our first, our first row here, we have our point, then we have our value for X, our value for Y, our value for X2, our value for Y2, and our value of X multiplied by Y. And going down our column for the point, we have 1 through 10, and then our value for sigma. And then we have all of our different values for X, Y, X squared, Y squad, and X multiplied by Y. So as we could see, when we substitute the values into our formula, we will find that R is going to be equal to drum roll. 10 multiplied by 144 minus 27 multiplied by 37, all divided by the square root of 10 multiplied by 123 minus 27 to the power of 2. And then we're gonna multiply this by the square root of 10, multiplied by 187 minus 37 to the power of 2. Fantastic, and that will mean when we plug into our calculator that R is going to be equal to 0.8. 802, which will mean that R will be approximately equal to because we're going to be routing to two decial places to match all of our multiple choice answers. That will mean that R is equal to 0.88, and that is our final answer, or rather one of our final answers. Hooray. And as you should recall and note, since the value of the correlation coefficient is close to 1, that will mean that there is a strong positive linear correlation between the two variables. So that will mean, without a doubt that our final answer has to be multiple choice answer letter B. Hooray, we did it. So now that we know that our final answer is multiple choice answer letter B. Let us look at our multiple choice answer. So our correct answer is multiple choice answer letter B, which once again is R is equal to 0.88, and there is a strong positive linear correlation. And that's it. We've officially solved for this problem. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Outlier Refer to the accompanying Minitab-generated scatterplot.

b. After identifying the 10 pairs of coordinates corresponding to the 10 points, find the value of the correlation coefficient r and determine whether there is a linear correlation.

Key Concepts

Outliers

Correlation Coefficient (r)

Linear Correlation

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