Question

(Bus and Subway Riders) The number of bus and subway riders in Washington, D.C., during the summer months is believed to be heavily tied to the number of tourists visiting the city. Data for the past 12 years were obtained below. No. of riders (Y) (100,000s) No. of tourists (X) (1,000,000s) 15 7 10 2 13 6 15 4 25 14 27 15 24 16 20 12 27 14 44 20 34 15 17 7 Use the Excel data (Bus and Subway Riders Data) to develop a regression model to predict the number of riders based on the number of tourists. Let Y = number of riders (in 100000s) and X = number of tourists (in 1000000s). (Bus and Subway Ridership) Find the correlation coefficient and coefficient of determination. (a) The correlation coefficient is ___. [Answer format: two decimal places] (b) ___% of the variation in the number of riders is explained by the number of tourists. (Hint: The answer is a percentage, e.g., 0.45 = 45%.) [Answer format: integer] Write your answer(s) as 1.23, 45

Answer 1

Answer:

a) 0.92; b) 84%

Step-by-step explanation:

First we enter the data into a graphing calculator.  Use the values for X, The number of tourists, in the first list and the values for Y, the number of riders, in the second list.

Bring up the scatter plot and then run the linear regression.  We get the equation

y = 1.59x + 5.06.

For part a,

The correlation coefficient, r, is 0.92.  This means the equation is a good fit for the data.

For part b,

The coefficient of determination, r², tells us what percentage of variation in the dependent variable, y, is explained by the independent variable, x.  This value is 0.84, which is 84%.