The following table gives the average weekly retail price of a gallon of regular gasoline in the eastern United States over a 9-week period from December 19, 2011, through February 13, 2012. Consider these 9 weeks as a random sample.

a. Assign a value of 0 to 12/19/11, of 1 to 12/16/11, of 2 to 01/02/12, and so on. Call this new variable Time. Make a new table with the variables Time and Price.
b. With time as an independent variable and price as the dependent variable, compute SSxx, SSyy, and SSxy.
c. Construct a scatter diagram for these data. Does the scatter diagram exhibit a linear positive relationship between time and price?
d. Find the least squares regression line Å· = a + bx
e. Give a brief interpretation of the values of a and b calculated in part d.
f. Compute the correlation coefficient r.
g. Predict the average price of a gallon of regular gasoline in the eastern United States for Time = 26. Comment on this prediction.
h. The following table gives the average weekly retail price of a gallon of regular gasoline in the eastern United States for the weeks 10/24/11 through 12/12/11.

Calculate the correlation coefficient and the least squares regression line for the 17-week period given in the two tables, assigning 10/24/11 a value of 0, 10/31/11 a value of 1, and so on. What happens to the value of the correlation coefficient? Create a scatter diagram along with the regression line for the data having time on the horizontal axis and price on the vertical axis. Use the diagram to explain how the values of r and b changed.

Transcribed Image Text:

Date 2/19/1 12/26/11 01/02/12 01/09/12 01/16/12 01/23/12 01/30/12 02/06/12 02/13/12 Price 3.26 3.264 3.322 3.419 3.436 3455 3.523 5 3.617 Date0/24/03/ 11/07/1 11/14/11 11/21/11 11/28/11 12/05/1 12/12/11 Price (S) 3447 3.424 3.401 3.414 3.364 3.308 3.286 3.298