Statistics PART ONE.
Running Head Statistics
Statistics
PARTONE.
Volume of service(y) 
Labor(x1) 
Supplies(x2) 
7 
4 
1 
8 
4 
1 
12 
7 
2 
11 
7 
2 
17 
9 
5 
20 
12 
8 
22 
13 
9 
24 
14 
9 
15.125 
8.75 
4.625 
(∑Y) 
(∑x1) 
(∑x2) 
Mean 
Standard deviation 

Volume of service(y) 
15.125 
6.512351 
Labor(x1) 
8.75 
3.918819 
Supplies(x2) 
4.625 
3.583195 
Thecorrelation that exists between labor and supplies: corr (rx1, x2)=0.9792
Thecorrelation between labor and volumes of service: corr (rx1, y) =0.9921
Thecorrelation between supplies and volume of service: corr (rx2, y)=0.9818
Usingthis information, we can compute “R” which denotes overallcorrelation between the three variables y, x1 and x2. According toCohen et al (2013), the correlation analysis shows how two or morevariables affect each other. The formula for computing R is given bythe following formula:
Where(ry, x1)2 denotes correlation between labor and volume of servicesquared, (rx1, x2) denotes correlation between labor and supplies,(ry, x2)2 denotes correlation between volume of service and suppliessquared, (rx1, x2)2 denotes correlation between labor and suppliessquared.
Substitutingthe value got from excel sheet 1, R=0.9927. This shows that thecombined correlation between the labor and supplies with volume ofservice is 0.9927. Since the value is close to one, it implies thatwhen labor and supplies are taken together, there is a perfectrelationship with volume of service.
At95% confidence interval, it is possible to establish whether laborand supplies are perfect predictors of volume service.
Inthis case, we employ regression whose formula is given by:
And
B1=
B2=
a=
WhereY is the dependent variable, a= Y intercept, B=change in labor orsupplies, X1= labor, X2=supplies, SDy= standard deviation for volumeservice, SDx1=standard deviation for labor, SDx2=standard deviationfor supplies.
Usingthe data provided, B1=1.265, B2= 0.472, a= 1.873…
Thereforethe regression formula used is denoted by:
Y=1.873+1.265X1+0.472X2
Thisimplies that:
Anincrease in one unit of labor leads to 1.265 increase in servicevolume
Anincrease in one unit of supplies leads to 0.472 increase in servicevolume.
Theaverage increase in service volume is 1.873 ceteris paribus.
PART2
Educationattainment
Individualposition
Weintroduce a dummy where D1 represents education attainment and D2represent the position
Theregression equation is given by:
Salary ($000) 
Years of experience 
D1 
D2 
D1D2 
24 
10 
0 
0 
0 
32 
8 
0 
0 
0 
42 
15 
1 
1 
1 
18 
7 
1 
1 
1 
38 
11 
0 
0 
0 
54 
17 
1 
1 
1 
44 
3 
0 
0 
0 
35 
7 
0 
0 
0 
43 
2 
1 
0 
0 
65 
12 
0 
0 
0 
51 
6 
1 
1 
1 
22 
14 
0 
0 
0 
37 
9 
0 
1 
0 
48 
22 
1 
0 
0 
73 
4 
0 
0 
0 
81 
17 
0 
0 
0 
40 
15 
0 
0 
0 
19 
13 
1 
1 
1 
47 
1 
0 
0 
0 
52 
7 
0 
0 
0 
Fromthe results of ANCOVA model shown in ANCOVA sheet in the exceldocument uploaded, the regression equation at 95% confidence intervalis given by:
24=32.98+0.33educationattainment+10.8 individual position
Thisimplies that: an increase in the level of education leads to 33%increment in individual salaries. A rise in individual’s positionleads to 10.8% increment in individuals salaries. Holding all otherfactors constant, the average salary is 32.98.
Reference
Cohen,J., Cohen, P., West, S. G., & Aiken, L. S. (2013). Appliedmultiple regression/correlation analysis for the behavioral sciences.Routledge.
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