In Exercise 23, add data for a child who is 6 years old and ha...

Question

In Exercise 23, add data for a child who is 6 years old and has a vocabulary of 900 words. Describe how this affects the correlation coefficient r.

Accepted Answer

I have your money. Glad to have you with us. Here's the next problem. A teacher is studying the relationship between the number of practice quizzes taken and final exam scores among students in a math class. The data for 10 students is shown below. And we see quizzes taken, X and exam score Y in two columns. And we see reading these left to right, we have, so I'll read the quizzes taken, and then the corresponding exam score. We have 3 and 65, 4 and 70, 5 and 75, 6 and 78, 7 and 80, 8 and 85, 9 and 88, 10 and 91, 11 and 94, 12 and 96. The correlation coefficient for this data is R equal to 0.98, indicating a strong positive linear relationship. The teacher then adds data for an 11th student who took only 2 quizzes, but scored 95 on the exam. How would this new data point likely affect the correlation coefficient R? The value of our decreases because the new point weakens the existing linear linear trend. The value of our increases because the new student scored very high. See the value of r stays the same because only 1 point was added. Or the value of r becomes zero because the new point is unrelated to the others. So one of these is really easy to rule out, and that would be choice D, the value of R becomes 0. Because a value of 0 for R would mean that the variables are completely unrelated. With no relationship at all, but we have a strong relationship, uh, indicated by 10 values, it's only 1, that's the outlier. So this wouldn't make our R value 0. Now, what do we notice about this added data? Well, it is quite an outlier, so we'll say, new data point is an outlier. Because we have only 2 quizzes taken, so lower than any of our X values, an exam score of 95, almost the highest score. So, definitely way out of where the others show a trend. So we would not expect the value of R to stay the same, which is choice C. Only 1 point was added, true, but 11 isn't a big sample, and this, uh, this new data point is quite an outlier. So we would expect R to change, even if not by a lot. And then to determine whether R decreases or increases, let's recall the meaning of R, and that is that it indicates the strength of the correlation between the two values, with 1 and negative 1 being the strongest correlation and 0 being nothing. Well, this strong correlation R equals 0.98, it's a very high correlation. Then we have this outlier. So, our value of R will decrease, choice A. Sorry, I wanted that circle to be blue. The value of our decreases because the new point weakens the existing trend, so it lowers the correlation. Choice B, value of our increases, we know that's incorrect. So, rule out choice B, then it says because the new students scored very high, but only increase R if we also saw a high number of quizzes taken corresponding with that high grade. Again, R would indicate the strength of the correlation, so only a new point that had an even stronger correlation would increase our R value. So, once again, we're given a table with values for number of quizzes and the exam score. We're told the coefficient correlation coefficient is 0.98. And if the teacher adds data, this outlying data that doesn't fit in with the trend of the other data, how would this new data point likely affect that correlation coefficient R? And the answer is choice A. The value of our decreases because the new point weakens the existing linear trend. See you in the next video.

In Exercise 23, add data for a child who is 6 years old and has a vocabulary of 900 words. Describe how this affects the correlation coefficient r.

Key Concepts

Correlation Coefficient (r)

Impact of Outliers

Linear Relationship

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