Question

Employees of an Australian public service were asked (in five subsequent years) to choose the five most important workplace factors that most affected how satisfied they were with their job. The following data show the percentage of employees who nominated the factor "opportunities for career development” in their top five, and a corresponding satisfaction rating measured using the percentage of employees who were very satisfied" or "satisfied" in their current workplace. Year Top Five (%) 38 Satisfaction Rating (%) 64 67 1. According to you, which variable should be the dependent one? Explain your answer. 2. Draw the corresponding scatter diagram and interpret it. 3. Find the equation for the line of best fit through the data. Do not forget to write down the estimated equation. Provide a table containing the underlying calculations. 4. Interpret the coefficients obtained in the question (3).

Answer 1

1)

Dependent Variable is Satisfaction Rating (%) represented by Y.

Independent Variable is Top Five (%) represented by X.

Satisfaction Rating is dependent because the Top five rating affects the satisfaction rating.

2)

Scatter Diagram

Using Excel<data<megastat<correlation/regression<Scatterplot

Satisfaction Rating (%)Y HHHHHHHHHHHHHHHHHHHHH 30 4050 60 70 Top Five (%)X

The scatterplot shows a positive and linear relationship between Top Five(%) and satisfaction Rating(%).

3)

Satisfaction Rating (%) Y y = 1.124 x + 19.075 R2 = 0.957 HHHHHHHHHHHHHHHHHHHHHHH 30 40 50 60 70 Top Five (%)X

	Top Five (%)X	Satisfaction Rating (%)Y	X^2	Y^2	XY
	30	49	900	2401	1470
	38	64	1444	4096	2432
	40	67	1600	4489	2680
	55	82	3025	6724	4510
	60	84	3600	7056	5040
Total	223	346	10569	24766	16132

Sample size = 5

SSX = Sxx => x2-9 -= 10569 – (223) -- = 623.2

SST = Syy = (3462 212 V) y2 -= 24766 -= 822.8 5

-δεν = 55x = 5ης - Σαν ΣεΣΥ - 16132 - 346 - 223 7004 n

Slope (bz) = $xy = 799.4 = 1.124

Intercept (be) = (Sy-b,5 x) = 346 – (1.124 * 223) – -= 19.075

The regression equation is:

y = 1.124x + 19.075

4)

Slope =1.124

The slopes indicate that with 1% increase in the top five (%), the Satisfaction Rating (%) is increased by 1.124%.

Intercept: 19.075

When the top five (%) is zero then the satisfaction rating is 19.075.

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