Please solve this in Stata or Excel data to check what is causing the variation
ID: 3247792 • Letter: P
Question
Please solve this in Stata or Excel
data to check what is causing the variation in the acid content in bones among 42 male skeletons from 2 cemeteries. The independent variables included are internment lengths, ages, depths, lime addition and contamination in soil.
Variables/Columns
Burial Site (1 or 2)
Internment Time (Years)
Burial Depth (feet)
LimeAdded (at internment) (1=Yes, 0=No)
Death_Age (Age of Person at the time of death)
Acid Level (g/100g of bone)
Contamination (In soil) (1=Yes, 0=No)
1.Undertake appropriate basic data analytics to motivate the regression model Use dummy variables for each of Burial Site, LimeAdded, and Contamination (If required create the dummy-variables for each).
2.Do you suspect any multicollinearity problem could affect the regression coefficients?
3.Run a regression model of the Acid Level on all independent variables provided and interpret all regression
4.Briefly describe what you need to do before conducting any hypothesis testing when you find evidence of heteroscedasticity in an OLS regression model? Test for heteroscedasticity to check for evidence of heteroscedasticity in part
5.Test the hypothesis that
Beta_InternmentTime < -0.00675
Jointly Beta_BurialSite = Beta_BurialDepth =Beta_LimeAdded=0
6. What is the best model specification that would explain acid content in bones better?
Burial Site
InternmentTime
Baurial Depth
Lime Added
Death_Age
Contamination
Acid Level
1
88.5
7
1
34
1
3.88
1
88.5
7
1
38
1
4
1
85.2
7
1
27
1
3.69
1
71.8
7.6
1
26
0
3.88
1
70.6
7.5
1
42
0
3.53
1
68
7
1
28
0
3.93
1
71.6
8
1
35
0
3.88
1
70.2
6
1
44
0
3.64
1
55.5
6
0
29
0
3.97
1
36.5
6.5
0
29
0
3.85
1
36.3
6.5
0
48
0
3.96
1
46.5
6.5
0
35
0
3.69
1
35.9
6.5
0
40
0
3.76
1
45.5
6.5
0
34
0
3.75
1
43
6.5
0
38
0
3.75
1
44.9
6.5
0
27
0
3.92
1
59.5
8
0
26
0
3.76
1
58.3
8
0
23
0
3.93
1
56.5
8
0
35
0
3.7
1
56.3
8
0
23
0
3.82
1
43
6.5
0
40
0
3.78
1
42.5
9
0
31
0
4
1
29
7.5
0
31
0
3.92
1
35.3
8.5
0
39
0
3.79
2
93.6
4
1
39
0
3.49
2
90
4
1
43
0
3.57
2
88
5.5
1
26
0
3.43
2
84.4
5
1
47
0
3.55
2
84
4.75
1
39
0
3.5
2
79.7
4.75
1
27
0
3.27
2
67.4
4.5
1
39
0
3.66
2
64.7
5
1
27
0
3.9
2
64.7
5.5
1
35
1
3.91
2
38.3
7
0
21
0
3.73
2
59.6
9.25
0
46
0
3.72
2
32
9
0
24
0
3.85
2
32.2
9
0
27
0
3.85
2
26.5
7
0
34
0
4.06
2
34.7
8.5
0
30
0
4.04
2
27.6
6
0
22
0
4
2
35.7
9
0
19
0
3.93
2
49.6
9
0
50
0
3.85
Burial Site
InternmentTime
Baurial Depth
Lime Added
Death_Age
Contamination
Acid Level
1
88.5
7
1
34
1
3.88
1
88.5
7
1
38
1
4
1
85.2
7
1
27
1
3.69
1
71.8
7.6
1
26
0
3.88
1
70.6
7.5
1
42
0
3.53
1
68
7
1
28
0
3.93
1
71.6
8
1
35
0
3.88
1
70.2
6
1
44
0
3.64
1
55.5
6
0
29
0
3.97
1
36.5
6.5
0
29
0
3.85
1
36.3
6.5
0
48
0
3.96
1
46.5
6.5
0
35
0
3.69
1
35.9
6.5
0
40
0
3.76
1
45.5
6.5
0
34
0
3.75
1
43
6.5
0
38
0
3.75
1
44.9
6.5
0
27
0
3.92
1
59.5
8
0
26
0
3.76
1
58.3
8
0
23
0
3.93
1
56.5
8
0
35
0
3.7
1
56.3
8
0
23
0
3.82
1
43
6.5
0
40
0
3.78
1
42.5
9
0
31
0
4
1
29
7.5
0
31
0
3.92
1
35.3
8.5
0
39
0
3.79
2
93.6
4
1
39
0
3.49
2
90
4
1
43
0
3.57
2
88
5.5
1
26
0
3.43
2
84.4
5
1
47
0
3.55
2
84
4.75
1
39
0
3.5
2
79.7
4.75
1
27
0
3.27
2
67.4
4.5
1
39
0
3.66
2
64.7
5
1
27
0
3.9
2
64.7
5.5
1
35
1
3.91
2
38.3
7
0
21
0
3.73
2
59.6
9.25
0
46
0
3.72
2
32
9
0
24
0
3.85
2
32.2
9
0
27
0
3.85
2
26.5
7
0
34
0
4.06
2
34.7
8.5
0
30
0
4.04
2
27.6
6
0
22
0
4
2
35.7
9
0
19
0
3.93
2
49.6
9
0
50
0
3.85
Explanation / Answer
Here dependent variable is acid level and there are five independent variables which are internment lengths, ages, depths, lime addition and contamination in soil.
Here we have to fit regression of dependent variable on independent variables.
Here the problem is of multiple regression.
We can do multiple regression in MINITAB.
steps :
ENTER data into MINITAB sheet --> Stat --> Regression --> Regression --> Response : Acid level --> Predictors : select all independent variables --> Options --> DIsplay : variance inflation factors --> ok --> Results : select second option --> ok --> ok
Output :
————— 7/13/2017 10:24:40 AM ————————————————————
Regression Analysis: Acid Level versus InternmentTi, Baurial Dept, ...
The regression equation is
Acid Level = 3.96 - 0.00641 InternmentTime + 0.0293 Baurial Depth
+ 0.0624 Lime Added - 0.00174 Death_Age + 0.234 Contamination
Predictor Coef SE Coef T P VIF
Constant 3.9621 0.1852 21.39 0.000
InternmentTime -0.006411 0.002039 -3.15 0.003 4.2
Baurial Depth 0.02927 0.01755 1.67 0.104 1.6
Lime Added 0.06238 0.08781 0.71 0.482 4.6
Death_Age -0.001743 0.002630 -0.66 0.512 1.1
Contamination 0.23398 0.07716 3.03 0.004 1.3
S = 0.130223 R-Sq = 53.6% R-Sq(adj) = 47.2%
Analysis of Variance
Source DF SS MS F P
Regression 5 0.70581 0.14116 8.32 0.000
Residual Error 36 0.61049 0.01696
Total 41 1.31631
Interpretation :
Intercept = 3.96
slopes :
b1 = coefficient of internment time = -0.00641
b2 = coefficient of baurial depth = 0.0293
b3 = coefficient of lime added = 0.0624
b4 = Coefficient of lime death age = -0.00174
b5 = coefficient of contamination = 0.234
Here we can test the hypothesis that,
H0 : Bj = 0 Vs H1 : Bj not= 0
where Bj is population slope for jth independent variable.
Assume alpha = level of significance = 0.05
Here test statistic follows F-distribution.
F = 8.32
P-value = 0.000
P-valua < alpha
Reject H0 at 0.05 level of significance.
Conclusion : Atleast one of the slope is differ than 0.
Also we can test individual significance.
Here we have to test the hypothesis that,
H0 : B = 0 Vs H1 : B not= 0
where B is population slope.
Here test statistic follows t-distribution.
Decision :
If P-value < alpha then reject H0 at 5% level of significance.
SO from the output we can say that lime added is insignificant variable and others are significant variable.
R-sq = 53.6%
It can expresses the proportion of variation in y which is explained by variation in independent variables.
Here all the VIF's are < 5. It indicates less multicollinearity problem.