Question

Bradford Electric Illuminating Company is studying the relationship between kilowatt-hours (thousands) used and the number of rooms in a private single-family residence. A random sample of 10 homes yielded the following. Number of Kilowatt-Hours Number of Kilowatt-Hours Rooms (thousands) Rooms (thousands) 12 9 8 6 9 7 10 8 14 10 10 10 6 5 5 4 10 8 7 7 a. Determine the regression equation. B. Determine the number of kilowatt-hours, in thousands, for a six-room house

Answer 1

For the regression equation and e the number of kilowatt-hours, in thousands, for a six-room house  is mathematically given as

Y = 1.33-0.667X and  5.3332

What is the number of kilowatt-hours, in thousands, for a six-room house?

Generally, the equation for the  standard deviation  is mathematically given as

$s$ₓ =$\sqrt{\frac{\sum\(X-\=X)^2}{n-1} }$

= $\sqrt{\frac{66.9}{10-1} }$

= 2.72

$s_y$ = $\sqrt{\frac{36.4}{10-1} }$

= 2.01

therefore correlation coff

r = $\frac{44.6}{(10-1)(2.72)(2.01)}$

r = 0.9038

In conclusion the regression equation is given

b = r_sy/sx

b = (0.9038)(2.01/2.72)

 = 0.667

intercept

a = 7.4-0.667(9.1)

a = 1.33

The regression equation is

Y = 1.33-0.667X

(b) number of kilowatts x = 6 house

Y = 1.33-0.667X

Y = 1.33-0.667(6)

 = 5.3332

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