Question

A corporation has offices in different parts of the country. It has gathered the following information concerning the number of bathrooms and the number of employees at seven sites. If a site has 1,150 employees, approximately how many bathrooms should it have? Number of employees x650730 810 900 102 107 1150 Number of bathrooms y 40 50 54 61 82 110 121 Table B25 Select one: a. 69 b. 91 c. 91,954 d. We should not be estimating here.

Answer 1

For the given dataset the no of employees x is the independent variable and the no of bathrooms is the dependent variable and to calculate the no of bathrooms for 1150 employees we need to find the regression equation. To calculate the regression equation we need to do the following table calculation as:

х Y X*Y X2 Y2 630 40 25200 396900 1600 730 50 36500 532900 2500 810 54 43740 656100 2916 900 61 54900 810000 3721 102 82 8364 10404 6724 107 110 11770 11449 12100 1150 121 139150 1322500 14641 Sum = 4429 518 319624 3740253 44202

Now the mean of both variables is calculated as:

77 X - X; - 4429 7 632.71428571429 n 1=1

72 Y = η ΣΥ, 518 7 = 74 1=1

Now the sum of squares is calculated as:

η η. SSxx = ΣΧ (ΣΧ; - 3740253 – 44292 / 7 = 937961.42857143 η 1=1 1=1

2 SSyy ΣΥ: Α (Σ Y; 44202 518' /7 = 5870

SSxy = ΣΧΥ, ΣΧ.Ε. - (Σκ) (Σ) 319624 - 4429 x 518/7 = -8122

Now the regression equation is computed as:

Y = n + m*X

Where the slope m and the intercept n is calculated as:

m= SSXY SSxx -8122 937961.42857143 0.0087

n = Ý - X: m = 74 – 632.71428571429 x (-0.0087) = 79.4788

Thus the regression equation is computed as:

Y = 79.4788 -0.0087X

Now using the equation the no of bathrooms for X = 1150 employees are calculated as:

Y=79.4788−0.0087* 1150

Y = 69.47

a) Thus Y = 69 bathrooms,