Question

The followings table gives information on GPAs (grade point average) and starting salaries (rounded to the nearest thousand dollars) of seven recent college graduates.  

GPA	2.90	3.81	3.20	2.42	3.94	2.05	2.25
Starting Salary	23	28	23	21	32	19	22

1) Predict the starting salary for a student graduating with a 3.60 GPA. (Enter your answer in thousands of dollars rounded to two decimal places. Such as 12,345.67)

2) Predict the starting salary for a student graduating with a 2.10 GPA. (Enter your answer in thousands of dollars rounded to two decimal places. Such as 12,345.67)

3) Predict the starting salary for a student graduating with a 3.95 GPA. (Enter your answer in thousands of dollars rounded to two decimal places. Such as 12,345.67)

Answer 1

From the given data

S.No. X^2 8.41 14.5161 10.24 5.8564 15.5236 4.2025 5.0625 63.8111 Y^2 529 784 529 441 2.9 3.81 3.2 2.42 3.94 2.05 2.25 20.57 XY 66.7 106.68 73.6 50.82 126.08 38.95 49.5 512.33 1024 361 484 4152 Total: 168

As per above table,

Mean i = = 20.57 7 = 2.9386 Meany - Σ' 168 ηΣ - (Σκ) Σν) byx= Σx - (Σκ) 1.512.33 - 20.57. 168 7. 63.8111 - (20.5702 3586.31 - 3455.76 446.6777 - 423.1249 130.55 23.5528 = 5.5429

Regression Line y on x y-] = byx(x - 1) y - 24 = 5.5429(x - 2.9386) y - 24 = 5.5429x - 16.2881 y = 5.5429x - 16.2881 + 24 y = 5.5429x + 7.7119

1) Given X = 3.6

Now Estimate y for x = 3.6 y=5.5429 x 3.6 + 7.7119 y = 19.9543 +7.7119 y = 27.6662

Predict the starting salary for a student graduating with a 3.60 GPA. is 27,666.21 dollars

2) Given X = 2.10

Now Estimate y for x = 2.1 y = 5.5429 x 2.1 + 7.7119 y = 11.64 + 7.7119 y = 19.3519

Predict the starting salary for a student graduating with a 2.10 GPA is 19,351.91 dollars

3) Given X = 3.95

Now Estimate y for x = 3.95 y = 5.5429 x 3.95 +7.7119 y = 21.8943 +7.7119 y = 29.6062

Predict the starting salary for a student graduating with a 3.95 GPA. is 29,606.21 dollars