Question

The height (sidewalk to roof) of notable tall buildings in America is compared to the number of stories of the building (beginning at street level). Find the equation for ŷ=a+bx using this data chart.

Height (in feet)	Stories
1050	58
428	27
362	26
529	40
790	60
401	22
380	38
1454	110
1127	100
700	46

Answer 1

Here we have given that

X : Height (in feet)

Y: Stories

Now we want to find the least square regression line

we know that

where Y is response variable and X is predictor variable

is intercept =

is slope=

First we find the sums

n=number of observations=10

= 1050+428 + 362+529+790+401+380+1454+1127+700=7221

= 58+27+26+40+60+22+38+110+100+4=485

X	Y	X^2	Y^2
1050	58	1102500	3364
428	27	183184	729
362	26	131044	676
529	40	279841	1600
790	60	624100	3600
401	22	160801	484
380	38	144400	1444
1454	110	2114116	12100
1127	100	1270129	10000
700	4	490000	16

we get and  

X	Y	XY
1050	58	60900
428	27	11556
362	26	9412
529	40	21160
790	60	47400
401	22	8822
380	38	14440
1454	110	159940
1127	100	112700
700	4	2800

Now,we find the and

=

=

=

=0.0769

=48.50 - 0.0769 * 722.10

= -7.029

we get the least square regression line is

= -7.029 + 0.0769 ( X)

where

and