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) Calculate the correlation coefficient. (Round to two decimal places)

2) What is the interpretation of the correlation coefficient?

A. The better GPA the student earns, the higher the starting salary the student will receive.

B. The higher the starting salary the student earns, the better the GPA will be for the student.

C. The lower the GPA the student earns, the higher the starting salary upon graduation.

3) Find the least squares regression line. (Four decimal places and just use y because you cannot do y hat)

4) 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)

5) 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)

6) 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

ΣX= 20.57   ΣY = 168   ΣX * Y = 512.33    ΣX2 = 63.8111 ΣY2 = 4152

Part 1

r = 0.93

Part 2

A. The better GPA the student earns, the higher the starting salary the student will receive.

Part 3

Equation of regression line is Ŷ = a + bX


b = 5.5429
a =( Σ Y - ( b * Σ X) ) / n
a =( 168 - ( 5.5429 * 20.57 ) ) / 7
a = 7.7119
Equation of regression line becomes Ŷ = 7.7119 + 5.5429 X

Part 4

When X = 3.6
Ŷ = 7.712 + 5.543 X
Ŷ = 7.712 + ( 5.543 * 3.6 )
Ŷ = 27.67

Part 5

When X = 2.1
Ŷ = 7.712 + 5.543 X
Ŷ = 7.712 + ( 5.543 * 2.1 )
Ŷ = 19.35

Part 6

When X = 3.95
Ŷ = 7.712 + 5.543 X
Ŷ = 7.712 + ( 5.543 * 3.95 )
Ŷ = 29.61