Question

The following data have to do with the relationship between maternal smoking (# of cigarettes smoked per day,

which is variable X) and infant birth weight (which is variable Y). (∑X, ∑X², ∑Y, ∑Y², and ∑XY have already been

calculated for you and are shown below in red font.)

Cigarettes Per Day (X) X²    Infant Birth Weight (Y) Y² XY

2                                                        4                                            7.5                                 56.25                             15.0

6                                                      36                                            7.2                                 51.84                             43.2

10                                                100                                            6.9                                 47.61                             69.0

12                                                  144                                            6.2                                 38.44                             74.4

14                                                196    5.8 33.64 81.2

∑X = 44                                        ∑X² = 480                              ∑Y = 33.6                      ∑Y² = 227.78             ∑XY = 282.8

What is the regression equation for this data?

Answer 1

let our regression equation be:Y=a+bX

from the data given above:

=44/5=8.8

=33.6/5=6.72

SS_xx===92.8

SS_yy===1.988

SS_xy===-12.88

b===-0.1387

a==6.72-(-0.1387)*8.8

a=6.72+0.1387*8.8=7.94

hence the regression equation:

Y=a+bX

Y=7.94-0.1387X

infant birth weight =7.94-0.1387*smoking (# of cigarettes smoked per day)

please rate my answer and comment for doubts.