14.50 Corporate political contributions, profits, and regression: Researchers studied whether corporate political contributions predicted profits (Cooper et al., 2007). From archival data, they determined how many political candidates each company supported with financial contributions, as well as each company’s profit in terms of a percentage. The accompanying table shows data for five companies. (Note: The data points are hypothetical but are based on averages for companies falling in the 2nd, 4th, 6th, and 8th deciles in terms of candidates supported. A decile is a range of 10%, so the 2nd decile includes those with percentiles between 10 and 19.9.)

Number of Candidates Supported Profit (%) 6 12.37 17 12.91 39 12.59 62 13.43 98 13.42

a. Create the scatterplot for these scores.

b. Calculate the mean and standard deviation for the variable “number of candidates supported.”

c. Calculate the mean and standard deviation for the variable “profit.”

d. Calculate the correlation between number of candidates supported and profit.

e. Calculate the regression equation for the prediction of profit from number of candidates supported.

f. Create a graph and draw the regression line. g. What do these data suggest about the political process? h. What third variables might be at play here? i. Compute the standardized regression coefficient. j. How does this coefficient relate to other information you know? k. Draw a conclusion about your analysis based on what you know about hypothesis testing with simple linear regression.