Question

The table shows the total square footage​ (in billions) of retailing space at shopping centers and their sales​ (in billions of​ dollars) for 10 years. The equation of the regression line is

ModifyingAbove y with caret equals 550.067 x minus 1890.986y=550.067x−1890.986.

Complete parts a and b.

Total Square​ Footage, x	4.94.9	5.25.2	5.35.3	5.45.4	5.55.5	5.75.7	5.75.7	5.85.8	6.16.1	6.26.2
​Sales, y	870.4870.4	938.4938.4	976.8976.8	1056.91056.9	1119.21119.2	1200.11200.1	1299.81299.8	1330.51330.5	1449.71449.7	1542.11542.1

​(a) Find the coefficient of determination and interpret the result.

nothing

​(Round to three decimal places as​ needed.)

Answer 1

Solution :

X	Y	XY	X^2	Y^2
4.9	870.4	4264.96	24.01	757596.16
5.2	938.4	4879.68	27.04	880594.56
5.3	976.8	5177.04	28.09	954138.24
5.4	1056.9	5707.26	29.16	1117037.61
5.5	1119.2	6155.6	30.25	1252608.64
5.7	1200.1	6840.57	32.49	1440240.01
5.7	1299.8	7408.86	32.49	1689480.04
5.8	1330.5	7716.9	33.64	1770230.25
6.1	1449.7	8843.17	37.21	2101630.09
6.2	1542.1	9561.02	38.44	2378072.4

n	10
sum(XY)	66555.06
sum(X)	55.80
sum(Y)	11783.90
sum(X^2)	312.82
sum(Y^2)	14341628.01
Numerator	8008.98
Denominator	8144.64
r	0.9833
r square	0.9670
Xbar(mean)	5.5800
Ybar(mean)	1178.3900
SD(X)	0.2494
SD(Y)	111.2445
b	550.0673
a	-1890.9856

r = 0.9833

(a)

coefficient of determination = r ² = 0.9833² = 0.967