[DATA] Graduation Rates PayScale reports statistics on college...

Question

[DATA] Graduation Rates PayScale reports statistics on colleges and universities. Go to www.pearsonhighered.com/sullivanstats to obtain the data file 11_3_24 using the file format of your choice for the version of the text you are using. The data contain the four-year cost and graduation rate for over 1300 colleges and universities. Do schools that charge more have higher graduation rates? The variable “4 Year Cost” represents the four-year cost of attending the college or university. The variable “Grad Rate” represents the percentage of incoming freshman who graduate within six years.
b. Determine the correlation coefficient between “4 Year Cost” and “Grad Rate.”

b. Determine the correlation coefficient between “4 Year Cost” and “Grad Rate.”

Accepted Answer

A researcher collects data on the number of hours students have been studying per week and their final exam scores for a sample of 8 students. The data are as follows, and we're given a table of values with their hours and exam scores. What is the correlation coefficient between study hours and exam score? We have four possible answers, 0.099. 0.991, 0.909, or 0.999. I have provided a table of values on the right here, which goes with our correlation coefficient equation. This equation is given as R equals. In multiplied By the sum of XY. M Sum of X multiplied by the sum of y. Divided by The square root Um Some of X squid Minus Sum of X all square. I multiply By in Some Of y square minus sum of all squared. Now we can plug this into our equation by looking at our table. This table has all of our sums for our equation. We have the X, which is the sum of all the X values, the Y, which is the sum of all Y values. We have the sum of X2, which means we square every X and add them together. The same for Y with the Y squared, and then XY is a product of X and Y, all summed together. From here we can plug this into our equation. Now we have N, which is 8, multiplied by the sum of XY, which is 8248. Minus the sum of X, which is 104. Multiplied by the sum of Y, which is 613. Divided by the square root Of 8 multiplied by the sum of X2, 1520. Minus the sum of X, which is 104. All square. All multiified by eights. Multiplying By the sum of Y247. 435. Minus Y squared Which will be 6:13. All's quick. Now we can plug this into a calculator, and this gives us a value of approximately 0.999. This is our correlation coefficient, which means the answer to our problem is answer D. OK, I hope to help you solve the problem. Thank you for watching. Goodbye.

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