After working with the data, you realize that since Half-Foods was acquired, its staffing and sales...

After working with the data, you realize that since Half-Foods was acquired, its staffing and sales strategies has changed quite drastically and therefore the historical data is not valid any more. Especially, there has been a significant reduction of staff. So you decide to collect new data from your stores. In the table below, you can find the average number of employees and the sales for each Half-Foods store in the past six months. Build a regression model that uses average number of employees to explain sales.

Average Number of Employees
8.74
9.42
10.2
6.81
15.31
6.14
6.68
11.3
6.36
13.74
12.57
9.77
19.79
23.64
11.24
5.32
13.41
15.3
20.94
21.88
24.43
6.18
16.67
1.2
1.11
4.69
9.1
12.49
23.67
10.13
5.76
21.84
4.1
0.07
21.82
9.79
21.44
10.77
5.4
5.49
24.41
11.53
5.71
25.97
8.97
10.93
16.72
2.59
15.86
21.93
5.72
15.14
18.39
0.1
13.25
8.85
17.25
23.54
22.01
7.31
12.2
11.2
16.35
16.18
14.81
22.48
25.07
18.66
13.41
4.61
3.94
22.6
12.02
18.04
24.8
24.74
9.03
23.5
10.87
22.82
6.17
18.04
22.61
16.31
20.11
21
19.25
14.98
17.25
0.01
6.91
11.5
2.48

Sales ($M)
149.95
150.05
136.3
129.25
177.18
96.32
160.9
120.28
110.63
149.05
175.98
150.29
193.63
319.17
170.51
111.55
129.16
181.5
280.74
234.75
248.49
77.78
142.72
65.22
46.04
93.74
171.14
98.06
347.57
176.19
43.89
318.41
112.32
41.18
272.37
84.75
329.2
75.87
91.38
30.33
312.43
150.53
111.12
360.98
93.97
162.18
215.79
91.23
271.51
285.16
130.16
319.84
262.94
63.24
240.44
122.23
285.24
293.39
318.12
63.61
157.51
148.61
184.38
279.23
187.97
345.79
362.55
281.03
205.33
51.46
97.1
220.72
134.85
257.46
321.77
415.03
74.08
277.87
191.98
266.27
157.43
225.1
303.17
148.61
198.18
298.13
214.34
230.61
219.41
96.03
168.33
155.29
67.64

Based on this analysis, how many additional sales (in $M) does an extra employee bring?

What is the p-value of the coefficient of Average Number of Employees?

Expert Solution

Independent variable (X): Average Number of Employees

Dependent variable (Y): Sales ($M)

Following is the output of regression analysis generated by excel:

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.89351455
R Square	0.79836825
Adjusted R Square	0.796152517
Standard Error	41.30716232
Observations	93

ANOVA
	df	SS	MS	F	Significance F
Regression	1	614803.6728	614803.6728	360.3178	2.12023E-33
Residual	91	155271.6309	1706.281659
Total	92	770075.3038

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	33.71137091	9.091222786	3.708122846	0.000359	15.65277407	51.769968
X	11.37178473	0.599081301	18.98203918	2.12E-33	10.18178335	12.561786

The required regression equation is

y' = 33.711 +11.372*x

That is for each additional employee sales is increased by 11.372 ($M) units.

The p-value of the coefficient of Average Number of Employees is 0.0000

orchestra answered 1 year ago

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After working with the data, you realize that since Half-Foods was acquired, its staffing and sales...

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