In an effort to explain variation in client profitability, an accounting firm collected the data shown in the accompanying table. The firm wants to know if it needs the client type in addition to the number y = Net profit earned from the client earned from the client. *1 = Number of hours spent working with the client a. Fit a model to the data that incorporates the number of hours spent working with the client and the type of client as independent variables. (Hint: Client type has three levels.) *2= Type of client (1 if manufacturing, 2 if service, b. Fit a second-order model to the data, using the same dummy variables for client type. Does this model provide a better fit than that found in part a? Which model would you recommend be used? Click the icon to view the data. y *1 X2 2,343 43 4,300 56 271 23 a. Since client type has three levels, use two dummy variables for client type, x2 = 1 if manufacturing, 0 otherwise and X3 = 1 if service, 0 otherwise. Complete the regression model below. 1,206 59 1,402 27 500 22 (Round the constant and the *2 and X3 coefficients to the nearest integer as needed. Round the x, coefficient to one decimal place as needed.) -700 37 3,456 47 b. Complete the regression model below. 2,474 47 1,974 22 204 34 (Round the constant and the x2 and x3 coefficients to the nearest integer as needed. Round the x, coefficient to one decimal place as needed. Round the x, coefficient to two decimal places as nee The adjusted R-squared value for the first-order model is and the adjusted R-squared value for the second-order model is . so model provides a better fit. (Round to three decimal places as needed.) Print Done For a = 0.05, significant in the first-order model. In the second-order model, significant. So in the dependent variable, client profitability. Therefore, recommend model