Question

In a certain dormitory, for various nights, we compare the number of residents who go to bed with their shoes on with the number who wake up in the morning with headaches. #sleep with shoes 10 12 8 20 16 5 15 20 #headaches 12 9 5 15 12 3 11 17 Find the correlation between these two variables: sum of X's: sum of X squared's: sum of Y's: sum of Y squared's: sum of X*Y's: SS(X)= SS(Y)= SS(XY)= All previous answers should be exact. The correlation r= (to seven places after the decimal) Compute the missing pieces of the linear regression line of headaches on sleeping with shoes (to five places after the decimal): Y-hat = X + For each x, write down the prediction y-hat (to one place after the decimal): For 13 people sleeping with their shoes on, we predict headaches. For 19 people sleeping with their shoes on, we predict headaches.

Answer 1

Find X⋅Y , X² and Y² as it was done in the table below.

X	Y	X⋅Y	X⋅X	Y⋅Y
10	12	120	100	144
12	9	108	144	81
8	5	40	64	25
20	15	300	400	225
16	12	192	256	144
5	3	15	25	9
15	11	165	225	121
20	17	340	400	289

• Answer :Correlation ( r ) = 0.9237664

• Answer : y = −0.06205+ 0.79714⋅x

Given x = 13 then

y = −0.06205+ 0.79714 ( 13 )

y = 10.30077

• Answer :   y = 10.30077

Given x = 19 then

y = −0.06205+ 0.79714 ( 19 )

y = 15.08361

• Answer : y = 15.08361