Question

7. I want you to do a partial correlation for the following data. Essentially, you have a correlation between the amount of hair a man has on his head and the digits he gets at the local bingo parlor, but one confound can be if he is working the room during the seafood or "pizass. from around the world" buffet days. I want you to remove the buffet variable from both the amount of male pattem balding and digits received. Is it a confound? Male Baldness and Digits −rxy=.12 Buffet type and Male Baldness −rxx =.78 Digits and Buffet −ry=.59

Answer 1

To remove the buffet variable from the correlation between male baldness and digits received, we need to calculate the partial correlation. The formula to do this is provided, using the given correlation coefficients.

Step-by-step explanation:

When conducting a partial correlation, the goal is to remove the influence of a third variable on the correlation between two other variables. In this case, the amount of hair a man has on his head and the digits he gets at the local bingo parlor are the variables of interest, and the buffet variable is the potential confound.

To determine if the buffet variable is a confound, we need to consider the correlation coefficients. The correlation between male baldness and digits received is -rxy = 0.12, the correlation between buffet type and male baldness is -rxx = 0.78, and the correlation between digits received and buffet type is ry = 0.59.

To remove the buffet variable from both the amount of male pattern balding and digits received, we need to calculate the partial correlations. The partial correlation between male baldness and digits received, controlling for buffet type, is given by:

rxy|xz = (rxy - rxyyxzryz) / sqrt((1 - rxy2)(1 - ryz2))

Using the given correlation coefficients, we can substitute the values and solve for the partial correlation.