Statistical Analysis Regression Multiple. Excel Capability

1. Income Household Amount
($1000s) Size Charged ($)
54 3 4,016
30 2 3,159
32 4 5,100
50 5 4,742
31 2 1,864
55 2 4,070
37 1 2,731
40 2 3,348
66 4 4,764
51 3 4,110
25 3 4,208
48 4 4,219
27 1 2,477
33 2 2,514
65 3 4,214
63 4 4,965
42 6 4,412
21 2 2,448
44 1 2,995
37 5 4,171
62 6 5,678
21 3 3,623
55 7 5,301
42 2 3,020
41 7 4,828
54 6 5,573
30 1 2,583
48 2 3,866
34 5 3,586
67 4 5,037
50 2 3,605
67 5 5,345
55 6 5,370
52 2 3,890
62 3 4,705
64 2 4,157
22 3 3,579
29 4 3,890
39 2 2,972
35 1 3,121
39 4 4,183
54 3 3,730

2. 23 6 4,127
27 2 2,921
26 7 4,603
61 2 4,273
30 2 3,067
22 4 3,074
46 5 4,820
66 4 5,149

3. Income Household
($1000s) Size
Mean 43.48 Mean 3.42
Standard Error 2.06 Standard Error 0.25
Median 42 Median 3
Mode 54 Mode 2
Standard Deviation 14.55 Standard Deviation 1.74
Sample Variance 211.72 Sample Variance 3.02
Kurtosis -1.25 Kurtosis -0.72
Skewness 0.1 Skewness 0.53
Range 46 Range 6
Minimum 21 Minimum 1
Maximum 67 Maximum 7
Sum 2174 Sum 171
Count 50 Count 50
Confidence Level(95.0%) 4.14 Confidence Level(95.0%) 0.49

4. Amount
Charged ($)
Mean 3964.06
Standard Error 132.02
Median 4090
Mode 3890
Standard Deviation 933.49
Sample Variance 871411.2
Kurtosis -0.74
Skewness -0.13
Range 3814
Minimum 1864
Maximum 5678
Sum 198203
Count 50
Confidence Level(95.0%) 265.3

5. SUMMARY OUTPUT
Regression Statistics
Multiple R 0.63
R Square 0.4
Adjusted R Square 0.39
Standard Error 731.71
Observations 50
ANOVA
df SS MS F Significance F
Regression
Residual
1
48
### ###
### 535404.25
31.75 0 ($1000
Total 49 ###
6000
Charged ($)
Coefficients
Standard Error t Stat P-value Lower 95% Upper 95%
4000
Amount
Intercept 2204 329.05 6.7 0 1542.4 2865.6
Income
($1000s) 40.48 7.18 5.63 0 26.04 54.92
2000
RESIDUAL OUTPUT 0
PROBABILITY OUTPUT
Predicted 10 20 30
Amount Amount
Charged Charged Inco
Observation ($) Residuals
Standard Residuals Percentile ($)
1 4389.91 -373.91 -0.52 1 1864 ($10
2 3418.39 -259.39 -0.36 3 2448
3 3499.35 1600.65 2.21 5 2477
4 4227.99 514.01 0.71 7 2514
5 3458.87 -1594.87 -2.2 9 2583
6 4430.39 -360.39 -0.5 11 2731
7 3701.75 -970.75 -1.34 13 2921
8 3823.19 -475.19 -0.66 15 2972
9 4875.66 -111.66 -0.15 17 2995
10 4268.47 -158.47 -0.22 19 3020
11 3215.99 992.01 1.37 21 3067
12 4147.03 71.97 0.1 23 3074
13 3296.95 -819.95 -1.13 25 3121
14 3539.83 -1025.83 -1.42 27 3159
15 4835.18 -621.18 -0.86 29 3348
16 4754.23 210.77 0.29 31 3579
17 3904.15 507.85 0.7 33 3586

6. 18 3054.07 -606.07 -0.84 35 3605
19 3985.11 -990.11 -1.37 37 3623
20 3701.75 469.25 0.65 39 3730
21 4713.75 964.25 1.33 41 3866
22 3054.07 568.93 0.79 43 3890
23 4430.39 870.61 1.2 45 3890
24 3904.15 -884.15 -1.22 47 4016
25 3863.67 964.33 1.33 49 4070
26 4389.91 1183.09 1.63 51 4110
27 3418.39 -835.39 -1.15 53 4127
28 4147.03 -281.03 -0.39 55 4157
29 3580.31 5.69 0.01 57 4171
30 4916.14 120.86 0.17 59 4183
31 4227.99 -622.99 -0.86 61 4208
32 4916.14 428.86 0.59 63 4214
33 4430.39 939.61 1.3 65 4219
34 4308.95 -418.95 -0.58 67 4273
35 4713.75 -8.75 -0.01 69 4412
36 4794.7 -637.7 -0.88 71 4603
37 3094.55 484.45 0.67 73 4705
38 3377.91 512.09 0.71 75 4742
39 3782.71 -810.71 -1.12 77 4764
40 3620.79 -499.79 -0.69 79 4820
41 3782.71 400.29 0.55 81 4828
42 4389.91 -659.91 -0.91 83 4965
43 3135.03 991.97 1.37 85 5037
44 3296.95 -375.95 -0.52 87 5100
45 3256.47 1346.53 1.86 89 5149
46 4673.27 -400.27 -0.55 91 5301
47 3418.39 -351.39 -0.49 93 5345
48 3094.55 -20.55 -0.03 95 5370
49 4066.07 753.93 1.04 97 5573
50 4875.66 273.34 0.38 99 5678

7. Income
($1000s) Residual Plot
2000
1000
Residuals
0
-1000
-2000
10 20 30 40 50 60 70
Income
Income
($1000s)
($1000s) Line Fit Plot
Lower 95.0%Upper 95.0%
1542.4 2865.6
26.04 54.92
Column C
Column B
30 40 50
6000
60 70
Normal Probability Plot
Income 5000
Charged ($)
4000
($1000s)
Amount
3000
2000
1000
0
0 20 40 60 80 100 120
Sample Percentile

9. umn C
umn B

11. SUMMARY OUTPUT
Regression Statistics
Multiple R 0.75
R Square 0.57
Adjusted R Square 0.56
Standard Error 620.79
Observations 50
ANOVA
df SS MS F
Regression 1 ### ### 62.8
Residual 48 ### 385383.99
Total 49 ###
Coefficients
Standard Error t Stat P-value
Intercept 2581.94 195.26 13.22 0
Household
Size 404.13 51 7.92 0
RESIDUAL OUTPUT
Predicted
Amount
Charged
Observation ($) Residuals
Standard Residuals
1 3794.33 221.67 0.36
2 3390.2 -231.2 -0.38
3 4198.45 901.55 1.47
4 4602.58 139.42 0.23
5 3390.2 -1526.2 -2.48
6 3390.2 679.8 1.11
7 2986.07 -255.07 -0.42
8 3390.2 -42.2 -0.07
9 4198.45 565.55 0.92
10 3794.33 315.67 0.51
11 3794.33 413.67 0.67
12 4198.45 20.55 0.03
13 2986.07 -509.07 -0.83
14 3390.2 -876.2 -1.43
15 3794.33 419.67 0.68
16 4198.45 766.55 1.25
17 5006.71 -594.71 -0.97

12. 18 3390.2 -942.2 -1.53
19 2986.07 8.93 0.01
20 4602.58 -431.58 -0.7
21 5006.71 671.29 1.09
22 3794.33 -171.33 -0.28
23 5410.84 -109.84 -0.18
24 3390.2 -370.2 -0.6
25 5410.84 -582.84 -0.95
26 5006.71 566.29 0.92
27 2986.07 -403.07 -0.66
28 3390.2 475.8 0.77
29 4602.58 -1016.58 -1.65
30 4198.45 838.55 1.36
31 3390.2 214.8 0.35
32 4602.58 742.42 1.21
33 5006.71 363.29 0.59
34 3390.2 499.8 0.81
35 3794.33 910.67 1.48
36 3390.2 766.8 1.25
37 3794.33 -215.33 -0.35
38 4198.45 -308.45 -0.5
39 3390.2 -418.2 -0.68
40 2986.07 134.93 0.22
41 4198.45 -15.45 -0.03
42 3794.33 -64.33 -0.1
43 5006.71 -879.71 -1.43
44 3390.2 -469.2 -0.76
45 5410.84 -807.84 -1.31
46 3390.2 882.8 1.44
47 3390.2 -323.2 -0.53
48 4198.45 -1124.45 -1.83
49 4602.58 217.42 0.35
50 4198.45 950.55 1.55

13. Household
Size Residual Plot
2000
1000
Residuals
0
-1000
-2000
0 1 2 3 4 5 6
Household H
Size Size
Significance F 6000
0
Charged ($)
4000
Amount
2000
0
Lower 95% Upper 95%
Lower 95.0%
Upper 95.0% 0 1 2 3
2189.34 2974.54 2189.34 2974.54 Hous
S
301.59 506.67 301.59 506.67
Normal
6000
5000
Charged ($)
4000
Amount
PROBABILITY OUTPUT 3000
2000
1000
Amount 0
Charged 0 20
Percentile ($) S
1 1864
3 2448
5 2477
7 2514
9 2583
11 2731
13 2921
15 2972
17 2995
19 3020
21 3067
23 3074
25 3121
27 3159
29 3348
31 3579
33 3586

14. 35 3605
37 3623
39 3730
41 3866
43 3890
45 3890
47 4016
49 4070
51 4110
53 4127
55 4157
57 4171
59 4183
61 4208
63 4214
65 4219
67 4273
69 4412
71 4603
73 4705
75 4742
77 4764
79 4820
81 4828
83 4965
85 5037
87 5100
89 5149
91 5301
93 5345
95 5370
97 5573
99 5678

15. Household
Size Residual Plot
2 3 4 5 6 7 8
Household Household
Size Size Line Fit Plot
6000
Charged ($)
4000
Amount
Column C
2000 Column B
0
0 1 2 3 4 5 6 7 8
Household
Size
Normal Probability Plot
6000
5000
Charged ($)
4000
Amount
3000
2000
1000
0
0 20 40 60 80 100 120
Sample Percentile

17. SUMMARY OUTPUT
Regression Statistics
Multiple R 0.91
R Square 0.83
Adjusted R Square 0.82
Standard Error 398.09
Observations 50
ANOVA
df SS MS
Regression 2 35250755.67 17625377.84
Residual 47 7448393.15 158476.45
Total 49 42699148.82
Coefficients Standard Error t Stat
Intercept 1304.9 197.65 6.6
Income
($1000s) 33.13 3.97 8.35
Household
Size 356.3 33.2 10.73
RESIDUAL OUTPUT
Predicted Amount
Observation Charged ($) Residuals Standard Residuals
1 4162.97 -146.97 -0.38
2 3011.49 147.51 0.38
3 3790.34 1309.66 3.36
4 4743.03 -1.03 0
5 3044.62 -1180.62 -3.03
6 3839.81 230.19 0.59
7 2887.12 -156.12 -0.4
8 3342.82 5.18 0.01
9 4916.87 -152.87 -0.39
10 4063.58 46.42 0.12
11 3202.12 1005.88 2.58
12 4320.47 -101.47 -0.26
13 2555.79 -78.79 -0.2
14 3110.89 -596.89 -1.53
15 4527.44 -313.44 -0.8
16 4817.47 147.53 0.38
17 4834.27 -422.27 -1.08

18. 18 2713.29 -265.29 -0.68
19 3119.05 -124.05 -0.32
20 4312.31 -141.31 -0.36
21 5496.93 181.07 0.46
22 3069.59 553.41 1.42
23 5621.29 -320.29 -0.82
24 3409.08 -389.08 -1
25 5157.43 -329.43 -0.84
26 5231.86 341.14 0.87
27 2655.19 -72.19 -0.19
28 3607.88 258.12 0.66
29 4212.91 -626.91 -1.61
30 4950 87 0.22
31 3674.15 -69.15 -0.18
32 5306.3 38.7 0.1
33 5265 105 0.27
34 3740.41 149.59 0.38
35 4428.04 276.96 0.71
36 4138.01 18.99 0.05
37 3102.72 476.28 1.22
38 3690.95 199.05 0.51
39 3309.68 -337.68 -0.87
40 2820.86 300.14 0.77
41 4022.28 160.72 0.41
42 4162.97 -432.97 -1.11
43 4204.74 -77.74 -0.2
44 2912.09 8.91 0.02
45 4660.43 -57.43 -0.15
46 4038.61 234.39 0.6
47 3011.49 55.51 0.14
48 3459.01 -385.01 -0.99
49 4610.5 209.5 0.54
50 4916.87 232.13 0.6

19. (
2000
1000
Residuals
0
-1000
-2000
10 2
F Significance F
111.22 0
P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
0 907.27 1702.54 907.27 1702.54
0 25.15 41.12 25.15 41.12
0 289.5 423.09 289.5 423.09

21. Income
($1000s) Residual Plot
2000
1000
Residuals
0 Income
-1000 ($1000s) Line Fit Plot
-2000 6000
10 20 30 40 50 60 70
5000
Income
4000 ($1000s)
Charged ($)
Amount
3000 Column C
2000 Column B
1000
0
10 20 30 Household
40 50 60 70
Size Residual Plot
Income
2000 ($1000s)
1000
Residuals
0
-1000 Household
-2000 Size Line Fit Plot
6000 0 1 2 3 4 5 6 7 8
Household
Charged ($)
4000
Amount
Size
Column C
2000 Column B
0
0 1 2 3 4 5 6 7 8
Household
Size