Question

Question 6. The mean nighttime temperatures (X) and the scores on an index of collective aggression (Y) are recorded for six urban areas:

Mean Nighttime Low	Index of collective Aggression
(in 0F)
73	51
82	63
90	67
60	35
51	23
40	20

(a) Draw a scatter diagram.

(b) Find the regression equation.

(c) Interpret the values of a and b.

(d) Predict the value of the index when the mean nighttime low is 80.

Answer 1

( a )  scatter diagram

( b )

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

X	Y	X⋅Y	X⋅X
73	51	3723	5329
82	63	5166	6724
90	67	6030	8100
60	35	2100	3600
51	23	1173	2601
40	20	800	1600

( b ) Regression equation

( c ) 1.044 estimated average increase in  Index of collective Aggression when mean nighttime low  increased 1 unit

25.738 estimated average decrease in y at x = 0

( d ) given x = 80

then

y = -25.738 + 1.044 ( 80 )

= 57.782

y = 57.782