Question

Suppose that you are interested in the extent to which family responsibilities are related to absences from work. You measured the number of young children living at home as well as the number of work absences in the past year for a sample of 10 employees. The data is shown in the table. Using the information that you see here, calculate the value of the slope. Which of the following values comes closest to your result? Case Number of young children at home Number of days absent from work in a year 4 4 4 4 10 10 ○ +4.83 -2.09 +3.05 O +1.12

Answer 1

	X	Y	X*Y	X2	Y2
	1	4	4	1	16
	4	7	28	16	49
	3	9	27	9	81
	2	3	6	4	9
	1	2	2	1	4
	0	3	0	0	9
	0	6	0	0	36
	3	4	12	9	16
	5	10	50	25	100
	2	2	4	4	4
Sum =	21	50	133	69	324

$SS_{XX} = \sum_{i=1}^{n} X_i^2 - \displaystyle\frac{1}{n}\left(\sum_{i=1}^{n} X_i\right)^2 = 69 - 21^2/10 = 24.9$
$SS_{YY} = \sum_{i=1}^{n} Y_i^2 - \displaystyle\frac{1}{n}\left(\sum_{i=1}^{n} Y_i\right)^2 = 324 - 50^2/10 = 74$
$SS_{XY} = \sum_{i=1}^{n} X_i Y_i - \displaystyle\frac{1}{n}\left(\sum_{i=1}^{n} X_i\right) \left(\sum_{i=1}^{n} Y_i\right) = 133 - 21 \times 50/10 = 28$

$\textup{\textbf{Slope}, a}=\frac{SS_{XY}}{SS_{XX}} = \frac{28}{24.9} = \textbf{+ 1.1245}$

$\textup{\textbf{Standard error of estimate}}=\sqrt{\frac{SS_{YY}-a*SS_{XY}}{n-2}}$

$=\sqrt{\frac{74-1.1245*28}{10-2}} = \textbf{2.3053}$