3. Mr. Fred G. Hire is the manager of human resources at Saint Luke's Medical Center. As part of his yearly report to the president of the center, he is required to present an analysis of the salaried employees. Because there are over 1,000 employees, he does not have the staff to gather information on each salaried employee, so he selects a sample of 30. For each employee, he records the monthly salary; service at Saint Luke's (in months); gender (1 = male, 0 = female); and whether the employee has a technical or clerical job. (Technical jobs are coded 1 and the clerical jobs are coded 0.) Below is the sample set with all the data. Sampled Monthly Salary Length of Age Gender Job Employee Service $1,769 93 42 $1,740 104 33 $1.941 104 42 $2,367 1.26 57 $2.467 98 30 $1.640 99 49 $1.756 94 35 4040-4. $1,706 46 $1,767 124 56 $1,200 73 23 $1,706 110 67 $1,985 90 36 $1.555 104 53 $1.749 81 29 $2.056 106 45 $1,729 113 55 $2,186 129 46 $1.858 97 39 $1.819 101 43 $1,350 91 35 $2.030 100 40 044044409046464090- $2.550 123 59 $1.544 88 30 $1,766 117 60 $1.937 107 45 $1,691 105 32 $1,623 86 33 $1,791 131 56 $2,001 95 30 $1 874 98 47a. Are monthly salary and employee age related? The table below - with squared values and sums given - may help you in the calculations. Perform the appropriate test Y (Salary) X (Age) Y-Squared X-Squared KY 1,769 42 3129361 1764 74298 1,740 33 3027600 1089 57420 1,941 42 3767481 1764 81522 2,367 57 5602689 3249 134919 2,467 30 6086089 900 74010 1,640 49 2689600 2401 80360 1,756 35 3083536 1225 61460 1,706 46 2910436 2116 78476 1,767 56 3122289 3136 98952 1,200 23 1440000 529 27600 1,706 67 2910436 4489 114302 1,985 36 3940225 1296 71460 1,555 53 2418025 2809 82415 1,749 29 3059001 841 50721 2,056 45 4227136 2025 92520 1,729 55 2989441 3025 95095 2,186 46 4778596 2116 100556 1,858 39 3452164 1521 72462 1,819 43 3308761 1849 78217 1,350 35 1822500 1225 47250 2,030 40 4120900 1600 81200 2,550 59 6502500 3481 150450 1,544 30 2383936 900 46320 1,766 60 3118756 3600 105960 1,937 45 3751969 2025 87165 1,691 32 2859481 1024 54112 1,623 33 2634129 1089 53559 1,791 56 3207681 3136 100296 2,001 30 4004001 900 60030 1,874 47 3511876 2209 88078 SUMS 55153 1293 103860595 59333 2401 185b. Are monthly salary and service length related? The table below - with squared values and sums given - may help you in the calculations. Perform the appropriate test. Y (Salary) X (Service Length) Y-Squared X-Squared XY 1769 93 3129361 8649 164517 1740 104 3027600 10816 180960 1941 104 3767481 10816 201864 2367 126 5602689 15876 298242 2467 98 6086089 9604 241766 1640 99 2689600 9801 162360 1756 94 3083536 8836 165064 1706 96 2910436 9216 163776 1767 124 3122289 15376 219108 1200 73 1440000 5329 87600 1706 110 2910436 12100 187660 1985 90 3940225 8100 178650 1555 104 2418025 10816 161720 1749 81 3059001 6561 141668 2056 106 4227136 1 1236 217936 1729 113 2989441 12769 195377 2186 129 4778596 16641 281994 1858 97 3452164 9409 180226 1819 101 3308761 10201 183719 1350 91 1822500 8281 122850 2030 100 4120900 10000 203000 2550 123 6502500 15129 313650 1544 88 2383936 7744 135872 1766 117 3118756 13689 206622 1937 107 3751969 11449 207259 1691 105 2859481 1 1025 177555 1623 86 2634129 7396 139578 1791 131 3207681 17161 234621 2001 95 4004001 9025 190095 1874 98 351 1876 9604 183652 SUMS 55153 3083 103860595 322655 5728962 c. If you conclude that salary and service length are related, develop the regression equation that shows the relationship between a person's salary and his/her time of service in the company. d. Estimate the salary for a person if his/her length of service is 100 months. How about the salary for a person who has been working for 10 years
