4. The following table contains 25 observations by year of these variables. year
ID: 2943134 • Letter: 4
Question
4. The following table contains 25 observations by year of these variables.
year
Revenue per dollar
Number of offices
Profit Margin
1
3.92
7298
0.75
2
3.61
6855
0.71
3
3.32
6636
0.66
4
3.07
6506
0.61
5
3.06
6450
0.7
6
3.11
6402
0.72
7
3.21
6368
0.77
8
3.26
6340
0.74
9
3.42
6349
0.9
10
3.42
6352
0.82
11
3.45
6361
0.75
12
13
14
15
16
17
18
19
20
21
22
23
24
25
3.58
3.66
3.78
3.82
3.97
4.07
4.25
4.41
4.49
4.70
4.58
4.69
4.71
4.78
6369
6546
6672
6890
7115
7327
7546
7931
8097
8468
8717
8991
9179
9318
0.77
0.78
0.84
0.79
0.70
0.68
0.72
0.55
0.63
0.56
0.41
0.51
0.47
0.32
e. At 95% confidence, is the regression model significant?
f. If in a given year, the number of offices is 9000 and revenue per dollar is $5, what would you expect the profit margin to be?
year
Revenue per dollar
Number of offices
Profit Margin
1
3.92
7298
0.75
2
3.61
6855
0.71
3
3.32
6636
0.66
4
3.07
6506
0.61
5
3.06
6450
0.7
6
3.11
6402
0.72
7
3.21
6368
0.77
8
3.26
6340
0.74
9
3.42
6349
0.9
10
3.42
6352
0.82
11
3.45
6361
0.75
12
13
14
15
16
17
18
19
20
21
22
23
24
25
3.58
3.66
3.78
3.82
3.97
4.07
4.25
4.41
4.49
4.70
4.58
4.69
4.71
4.78
6369
6546
6672
6890
7115
7327
7546
7931
8097
8468
8717
8991
9179
9318
0.77
0.78
0.84
0.79
0.70
0.68
0.72
0.55
0.63
0.56
0.41
0.51
0.47
0.32
Explanation / Answer
One-way ANOVA: Revenue per dollar, Number of offices, Profit Margin Source DF SS MS F P Factor 2 873881660 436940830 1302.46 0.000 Error 72 24154168 335475 Total 74 898035828 S = 579.2 R-Sq = 97.31% R-Sq(adj) = 97.24% Level N Mean StDev Revenue per dollar 25 3.9 0.6 Number of offices 25 7243.3 1003.2 Profit Margin 25 0.7 0.1 Individual 95% CIs For Mean Based on Pooled StDev Level -+---------+---------+---------+-------- Revenue per dollar (*) Number of offices (*) Profit Margin (*) -+---------+---------+---------+-------- 0 2000 4000 6000 Pooled StDev = 579.2 e. At a 95% confidence, the regression model is significant (note: p-value is < 0.0001). f. The profit margin is expected to be 0.046. (See below). Regression Analysis: Profit Margin versus Revenue per dollar The regression equation is Profit Margin = 1.33 - 0.169 Revenue per dollar Predictor Coef SE Coef T P Constant 1.3262 0.1386 9.57 0.000 Revenue per dollar -0.16913 0.03559 -4.75 0.000 S = 0.100891 R-Sq = 49.5% R-Sq(adj) = 47.4% Analysis of Variance Source DF SS MS F P Regression 1 0.22990 0.22990 22.59 0.000 Residual Error 23 0.23412 0.01018 Total 24 0.46402 Revenue per Profit Obs dollar Margin Fit SE Fit Residual St Resid 4 3.07 0.6100 0.8069 0.0344 -0.1969 -2.08R 25 4.78 0.3200 0.5177 0.0387 -0.1977 -2.12R Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 0.4805 0.0455 (0.3864, 0.5747) (0.2515, 0.7095) Values of Predictors for New Observations Revenue per New Obs dollar 1 5.00Related Questions
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