Question

In order for applicants to work for the foreign-service department, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that applicants have studied a particular language and the grades they received on the proficiency exam.

# of years,x	2	3	3	4	5	5	6	6	8
Grade on test,y	59	62	70	72	78	85	80	88	92

Find the equation of the regression line for the given data.

Group of answer choices

= 49.61x + 5.7

= 49.61x - 7.08

= 7.08x - 49.61

= 5.7x + 49.61

Answer 1

ΣX = 42
ΣY = 686
ΣX * Y = 3361
ΣX2 = 224
ΣY2 = 53326

Equation of regression line is Ŷ = a + bX

b = (nΣΧΥ – ΣΧΣΥ)/(ηΣΧ? - (ΣΧ)2)


b = 5.702
a =( Σ Y - ( b * Σ X) ) / n
a =( 686 - ( 5.7024 * 42 ) ) / 9
a = 49.611
Equation of regression line becomes Ŷ = 49.61 + 5.7 X

= 5.7x + 49.61