Question

manager of a product sales group believes the number of sales made by an employee (Y) Hepends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of 8 employees provides the following Employee Y 1 100 2 90 3 80 4 70 5 60 6 50 7 40 30 X1 X2 107 3 10 8 9 5 4 5 8 7 5 1 4 1 1

Answer 1

Solution:

B) 3.103

Explanation:

Multiple regression using matrix method,

These are the data that have been provided for the dependent and independent variables: w 0 0 0 v = = The following matrix and vector are defined in order to conduct the matrix calculation required to compute the estimated multiple regression coefficients:

1 3 10 1 5 4 X = 1 y= 1 7 5 1 1 4 1 1 1 Now, the vector with the estimated regression coefficients ß is computed through the following matrix operation: B = (X'X)-?X'y Now, for the values provided for X and y, we get that the vector with estimated regression coefficients is computed as follows:

B = (X'X)-X'y 1 10 27-1 1 3 11 8 [ 1 1 1 1 1 1 1 1] [1 1 1 1 1 1 1 1] 1 5 10 3 8 5 5 7 1 1 10 3 8 5 5 7 1 1 1 5 8 7 10 9 4 8 5 4 1 7 10 9 4 8 5 4 1 7 1 1 4 1 1 1

40 48 「8 40 48| 40 274 272] | | 2980 48 272 352 3520 「0.756466 -0.034483 -0.076509] [520] -0.034483 0.017241 -0.008621 2980 -0.076509 -0.008621 0.019935 | 3520 「21.2931] [B] 3.1034 4.6983

Thus, you can see b1=3.1034