Question

Calculate the Coefficient of Correlation and the Least Squares Equation for the following data, hours of study (x) and hours of sleep(y). Using your equation, if the hours of study is 5, what is the expected hours of sleep? For any credit, make sure you show your work and submit a PDF or picture of it via the test assignment in Week 5. Hours of Study Hours of Sleep 2 10 6 6 6 5 3 9 2 12

Answer 1

	Hours of Study	Hours of Sleep	X * Y	X2	Y2
	X	Y
	2	10	20 (2*10)	4	100
	6	6	36 (6*6)	36	36
	6	5	30 (6*5)	36	25
	3	9	27 (3*9)	9	81
	2	12	24 (2*12)	4	144
Total	19	42	137	89	386
Average	3.8	8.4

Least Square equation is as follows

Y = mX + b

Where, X represents hours of study

Y represents hours of sleep

Where, m is slope of the line

b is Y intercept

To calculate m

m =

m =  

m = - 1.345

To calculate b

b =

b =

b = 13.512

Putting this values in the equation

Y = mX + b

Y = -1.345 X + 13.512

If the hours of study is 5, what is the expected hours of sleep?

We have, hours of study X = 5, find Y

Y = -1.345 X + 13.512

Y = -1.345 *5 + 13.512

Y = 6.786 7

if the hours of study is 5, will require 7 hours of sleep.

Coefficient of Correlation

Hours of Study	Hours of Sleep
X	Y
2	10	-1.8	1.6	-2.88	3.24	2.56
6	6	2.2	-2.4	-5.28	4.84	5.76
6	5	2.2	-3.4	-7.48	4.84	11.56
3	9	-0.8	0.6	-0.48	0.64	0.36
2	12	-1.8	3.6	-6.48	3.24	12.96
19	42	0	0	-22.6	16.8	33.2
3.8	8.4

r = - 0.957