Online stock trading. Online stock trading has increased dramatically during the past several years. An article discussing this new method of investing provided data on the major Internet stock brokerages who provide this service.9 Below are some data for the top 10 Internet brokerages.

The variables are Mshare, the market share of the firm; Accts, the number of Internet accounts in thousands; and Assets, the total assets in billions of dollars. These firms are not a random sample from any population, but we will use multiple regression methods to develop statistical models that relate assets to the other two variables.

ID Broker Mshare Accts Assets 1 Charles Schwab 27.5 2500 219.0 2 E*Trade 12.9 909 21.1 3 TD Waterhouse 11.6 615 38.8 4 Datek 10.0 205 5.5 5 Fidelity 9.3 2300 160.0 6 Ameritrade 8.4 428 19.5 7 DLJ Direct 3.6 590 11.2 8 Discover 2.8 134 5.9 9 Suretrade 2.2 130 1.3 10 National Discount Brokers 1.3 125 6.8

(a) Plot assets versus accounts and describe the relationship.

(b) Perform a simple linear regression to predict assets from the number of accounts. Give the least-squares line and the results of the hypothesis test for the slope.

(c) Obtain the residuals from part

(b) and plot them versus accounts. Describe the plot. What do you conclude?

(d) Construct a new variable that is the square of the number of accounts. Rerun the regression analysis with accounts and the square as explanatory variables. Summarize the results.