Question

Use the following information to answer questions 15 to 19.

The following indicates the number of hours that Johnny spent studying the week before each exam in his classes along with the corresponding exam scores:
Hours Studying:  4    5    8  12  15  19
Score on Exam:  54  49 60  70  81 94

Find the LSRL for this data.

a) y=2.87−37.86x

b) y=2.87x+37.86

c) y=12.5367x+0.3388

d) y=0.3388x−12.5367

e) y=37.86x+2.87

Answer 1

The number of hours that Johnny spent studying the week before each exam in his classes along with the corresponding exam scores:

Hours Studying (Xi)	4	5	8	12	15	19
Score on Exam (Yi)	54	49	60	70	81	94

Now we want find LSRL (Least Squares Regression Line) or this data.

LSRL (Least Squares Regression Line) given by,  Y = a + bX

where Y = dependent variable = Score on Exam , X= independent variable = Hours Studying and a , b are estiamted by least square method.

Least Square Estimate:

and   

Table for calculation:

4	54	-6.5	-14	91	42.25
5	49	-5.5	-19	104.5	30.25
8	60	-2.5	-8	20	6.25
12	70	1.5	2	3	2.25
15	81	4.5	13	58.5	20.25
19	94	8.5	26	221	72.25
Total=63	Total=408			Total=498	Total=173.5

Formula:

n = number of observation

and

Calculation:-

[ putting the value of Cov(X,Y) and Var(X) and round to two decimal places ]

[ putting the value of  and round to two decimal places ]

Now LSRL (Least Squares Regression Line) is given by,

Y = 2.87X + 37.86 i.e Marks = 2.87 Hours + 37.86

Answer:- Correct Answer is " Option b). Y = 2.87X + 37.86 "