Moraine Valley Community College Business Statistics Worksheet

I have attached two files. One of the files is the questions and the other file is the data needed to solve the questions.

SUMMARY OUTPUT
Wages on LOS
Regression Statistics
Multiple R
0,353
R Square
0,125
Adjusted R Square
0,110
Standard Error
82,233 $ per week
Observations
59
latest edit: 12-Nov.-2016
ANOVA
df
Regression
Residual
Total
SS
55034,359
385453,641
440488,000
1
57
58
MS
55034,36
6762,34
F
8,138
P-value
0,006
s=
Coefficients
Standard Error
t Stat
P-value Lower 95%
Intercept
349,4
18,096
19,31
0,000
313,140
LOS
0,5905
0,207
2,85
0,006
0,176
The regression equation is
Wages = 349.4 + 0.5905*LOS
SUMMARY OUTPUT
Regression:
82,23 $ / wk
Upper 95%
385,616
1,005
Wages on SIZE and LOS
Regression Statistics
Multiple R
0,540
R Square
0,291
Adjusted R Square
0,266
Standard Error
74,664 $ per week
Observations
N = 59
ANOVA
Regression
Residual
Total
df
SS
MS
2 128302,1886 64151,09
56 312185,8114
5574,75
N-1 = 59-1 = 58
440488,0000
Intercept
SIZE
LOS
Coefficients Standard Error
302,5446
20,9012
71,7751
19,7984
0,6681
0,1891
TABLE.
Wages on 3 Xs
F Significance F
11,51
0,0001
s^2 =
s =
t Stat
P-value Lower 95% Upper 95%
14,48 0,0000 260,6745
344,4146
3,63 0,0006 32,1142
111,4360
3,53 0,0008
0,2892
1,0470
5574,75
74,66 $ / wk
SUMMARY OUTPUT
Wages on SIZE, LOS, LOS*SIZE
Regression Statistics
Multiple R
0,553
R Square
0,306
Adjusted R Square
0,268
Standard Error
74,546 $ per week
Observations
59
ANOVA
df
Regression
Residual
Total
Intercept
SIZE
LOS
LOS*SIZE
3
55
58
SS
134848,108
305639,892
440488,000
MS
44949,37
5557,09
Coefficients
289,19
101,05
0,841
-0,416
Standard Error
24,228
33,442
0,247
0,383
t Stat
11,94
3,02
3,40
-1,09
F
8,089
P-value
0,000
s=
P-value Lower 95%
0,000
240,631
0,004
34,032
0,001
0,346
0,283
-1,184
The regression equation is
Wages = 289.19 + 101.051*SIZE + 0.841*LOS – 0.416*LOS*SIZE
or
289.18 + 0.841*LOS
if SIZE = 0 (small)
and
390.24 + 0.425*LOS
if SIZE = 1 (large)
Upper 95%
337,739
168,071
1,336
0,352
74,55 $ / wk
bankwage.xls
latest edition 2012: Nov. 28
next-to-latest revision 2011: May 28
n = 59
employees
at banks
(married women holding customer service jobs at Indiana banks)
TABLE. Description of Variables
Variable
Abbreviation
Variable Name
Units
WAGES
Wages dollars per week
LOS Length of Service
months
BANKSIZE
Bank Size
(0,1) variable
TABLE.
WAGES
389
395
Format of Data
LOS(mos.)
94
48
BANKSIZE
Large
Small
.
.
.
.
.
.
.
.
.
415
WAGES
102
LOS
(mos.)
Large
BANKSIZE
TABLE. Plan of Analysis: Three regressions are fitted: -Wages on LOS
Wages on LOS and SIZE
Wages on LOS, SIZE and LOS*SIZE
They can be ranked by Adjusted R-sq
(and equivalently by s, the square root of the residual mean square).
WAGES
389
395
329
295
377
479
315
316
324
307
403
378
348
488
391
541
312
418
417
516
443
353
349
499
322
408
393
277
649
272
486
393
311
316
384
360
369
529
270
332
547
347
328
327
320
404
443
261
417
450
443
566
461
436
321
221
547
362
415
SIZE
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
LOS
94
48
102
20
60
78
45
39
20
65
76
48
61
30
108
61
10
68
54
24
222
58
41
153
16
43
96
98
150
124
60
7
22
57
78
36
83
66
47
97
228
27
48
7
74
204
24
13
30
95
104
34
184
156
25
43
36
60
102
LOS*SIZE
94
0
0
0
60
0
45
39
20
0
76
0
0
30
108
61
0
68
54
24
0
58
0
153
0
0
96
98
150
0
60
7
0
57
78
36
0
66
0
0
0
27
0
7
0
204
24
0
30
95
104
34
0
0
25
0
36
0
102
BANKSIZE
Large
Small
Small
Small
Large
Small
Large
Large
Large
Small
Large
Small
Small
Large
Large
Large
Small
Large
Large
Large
Small
Large
Small
Large
Small
Small
Large
Large
Large
Small
Large
Large
Small
Large
Large
Large
Small
Large
Small
Small
Small
Large
Small
Large
Small
Large
Large
Small
Large
Large
Large
Large
Small
Small
Large
Small
Large
Small
Large
TABLE.
WAGES
LOS
Means
391,00
20332
70,49
5,87
$ per week
$ per year
months
years
Bin
25
50
75
100
125
150
175
200
225
Histogram for LOS (months)
16
14
12
10
8
6
4
2
0
100,00%
90,00%
80,00%
70,00%
60,00%
50,00%
40,00%
30,00%
20,00%
10,00%
,00%
25
50
75
100
125
150
175
200
225
More
Frequency
More
Frequency Cumulative %
11
18,33%
15
43,33%
13
65,00%
9
80,00%
5
88,33%
1
90,00%
2
93,33%
1
95,00%
2
98,33%
1
100,00%
Bin
SUMMARY OUTPUT
Wages on LOS
Regression Statistics
Multiple R
0,353
R Square
0,125
Adjusted R Square
0,110
Standard Error
82,233 $ per week
Observations
59
ANOVA
df
Regression
Residual
Total
Intercept
LOS
1
57
58
SS
MS
55034,359 55034,36
385453,641
6762,34
440488,000
CoefficientsStandard Error
349,4
18,096
0,5905
0,207
The regression equation is
F
P-value
8,138
0,006
s=
t Stat
P-value Lower 95% Upper 95%
19,31
0,000 313,140
385,616
2,85
0,006
0,176
1,005
Wages = 349.4 + 0.5905*LOS
82,23 $ / wk
SUMMARY OUTPUT
Regression:
Wages on SIZE and LOS
Regression Statistics
Multiple R
0,540
R Square
0,291
Adjusted R Square
0,266
Standard Error
74,664 $ per week
Observations
N = 59
ANOVA
df
Regression
Residual
Total
Intercept
SIZE
LOS
2
56
N-1 = 59-1 = 58
SS
MS
128302,1886 64151,09
312185,8114 5574,75
440488,0000
Coefficients
Standard Error
302,5446
20,9012
71,7751
19,7984
0,6681
0,1891
F
Significance F
11,51
0,0001
t Stat
P-value
14,48 0,0000
3,63 0,0006
3,53 0,0008
s^2 =
s =
Lower 95%
Upper 95%
260,6745
344,4146
32,1142
111,4360
0,2892
1,0470
5574,75
74,66 $ / wk
SUMMARY OUTPUT
Regression:
Wages on SIZE, LOS, and LOS*SIZE
Regression Statistics
Multiple R
0,553
R Square
0,306
Adjusted R Square
0,268
Standard Error
74,546 $ per week
Observations
59
ANOVA
df
Regression
Residual
Total
Intercept
SIZE
LOS
LOS*SIZE
3
55
58
SS
MS
134848,108 44949,37
305639,892 5557,09
440488,000
Coefficients Standard Error
289,185
24,228
101,051
33,442
0,841
0,247
-0,416
0,383
F
8,089
P-value
0,000
t Stat
P-value Lower 95% Upper 95%
11,94
0,000
240,631
337,739
3,02
0,004
34,032
168,071
3,40
0,001
0,346
1,336
-1,09
0,283
-1,184
0,352
For SIZE = 0 (small banks), the fitted value of Wages is 289.18 + 0.841 LOS
For SIZE = 1 (large banks), the fitted value of Wages is 289.18 + 101.051 + (0.841-0.416) LOS
or 390.23 + 0.425 LOS
Initial salary corresponds to LOS = 0. The initial salary is one hundred dollars higher in large banks,
but the increment for LOS is only .425 per month instead of 0.841 per month for small banks.