2.4 Exercise Set

Match each scatterplot shown below with one of the four specified correlation coefficients.

- c (-0.26) ? - a (-0.04) ? - b (0.93) -d (-1.00)

Based on the data shown below, calculate the correlation coefficient (to three decimal places) r =

-.924

The correlation coefficient, r, is a number between

-1 and 1

Here is a bivariate data set. Find the correlation coefficient and report it accurate to three decimal places. r =

.519

You generate a scatter plot using Excel. You then have Excel plot the trend line and report the equation and the r^2 value. The regression equation is reported as y= 29.95x + 41.87 and the r^2 = 0.4761 What is the correlation coefficient for this data set? r =

.69

Recently a community college offered a 2-credit course to help students with math anxiety. At the beginning of the course, each student took a 30-question survey (called MARS-S); the higher the score, the more anxiety experienced by the student. The nine students remaining in the class took the same survey at the end of the course. The before and after scores for each of the nine students who completed the course are shown below. Compute the correlation between before and after scores for these students. (Assume the correlation conditions have been satisfied and round your answer to the nearest 0.001.)

0.588

Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as y = -15.58x + 34.57 and the r = -.53 What proportion of the variation in y can be explained by the variation in the values of x? r^2 = % Report answer as a percentage accurate to one decimal place.

28.1

Choose the most appropriate completion of the sentence. In order to indicate a strong correlation between variables, the correlation coefficient will be

near -1 or 1

Here is a bivariate data set. Find the correlation coefficient and report it accurate to three decimal places. r = What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. r^2 =

r = .643 r^2 = 41.4

The following bivariate data set contains an outlier. What is the correlation coefficient with the outlier? rw = What is the correlation coefficient without the outlier? rwo = Does including the outlier change the linear correlation by at least 0.10?

rw = -.927 rwo = -. 168 Yes. Including the outlier changes the linear correlation by at least 0.10.