FACULTY OF ENGINEERING ELECTRICITY AND ELECTRONICS

ENGINEERING STATISTICS(BWM 20502)

PROJECT

GROUP 10 MEMBERS : RAJA FAIRUZ NABILA BINTI MUDZAFAR SHAH

(CE100202)SITI HAWA BINTI AWANG

(CE100068)AMANINA BINTI MUHAMAD SANUSI

(CE100124)NORKARLINA BINTI KHAIRUL ARIFFIN

(CE100154)HANISAH BINTI MUHAMAD AZLAN

(CE100172)IVY KENAI ROBERT

(CE100180)NURUL SYAUQEEN BINTI MUSTAFA

(CE100190)

NAME OF LACTURER: KHUNESWARI A/P P GOPAL PILLAY

QUESTION 10The purpose of this study is to see the relation between the percent of body fat with various body circumference measurements. Percentage of body fat for an individual can be estimated once body density has been determined. Folks (e.g. Siri (1956)) assume that the body consists of two components - lean body tissue and fat tissue. The 40 data of percent body fat from Siri's (1956) equation and weight (lbs) are shown below.

NO Weight (LBS), x Body Fat (%), y xy x² y²1 175.5 15.4 2702.7 30800.25 237.162 177.75 20.4 3626.1 31595.0625 416.163 161.25 20.5 3305.625 26001.5625 420.254 171.25 24.4 4178.5 29326.5625 595.365 163.75 11.4 1866.75 26814.0625 129.966 150.25 38.1 5724.525 22575.0625 1451.617 190.25 32.3 6145.075 36195.0625 1043.298 170.75 30 5122.5 29155.5625 9009 162.75 21.5 3499.125 26487.5625 462.25

10 180 13.8 2484 32400 190.4411 156.25 6.3 984.375 24414.0625 39.6912 227.75 12.9 2937.975 51870.0625 166.4113 199.5 24.3 4847.85 39800.25 590.4914 155.5 15.2 2363.6 24180.25 231.0415 215.5 30.2 6508.1 46440.25 912.0416 134.25 11 1476.75 18023.0625 12117 201 33.6 6753.6 40401 1128.9618 186.75 29.3 5471.775 34875.5625 858.4919 190.75 26 4959.5 36385.5625 67620 207.5 31.9 6619.25 43056.25 1017.6121 178.25 19.1 3404.575 31773.0625 364.8122 163 15.2 2477.6 26569 231.0423 175.25 15.6 2733.9 30712.5625 243.3624 158 19.5 3081 24964 380.2525 177.25 47.5 8419.375 31417.5625 2256.2526 179 13.6 2434.4 32041 184.9627 191 7.5 1432.5 36481 56.2528 199.25 24.5 4881.625 39700.5625 600.2529 218.75 27.3 5971.875 47851.5625 745.2930 217 20.4 4426.8 47089 416.1631 166.25 20.1 3341.625 27639.0625 404.0132 224.75 22.3 5011.925 50512.5625 497.2933 228.25 25.4 5797.55 52098.0625 645.1634 172.75 18 3109.5 29842.5625 32435 152.25 19.3 2938.425 23180.0625 372.4936 125.75 0.7 88.025 15813.0625 0.4937 177.25 20.5 3633.625 31417.5625 420.2538 176.25 16.9 2978.625 31064.0625 285.6139 363.15 35.2 12782.88 131877.9225 1239.0440 203 32.6 6617.8 41209 1062.76Σ 7424.6500 869.7000 167141.3050 1434050.2975 22317.9300

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.413673846

R Square 0.171126051

Adjusted R Square 0.149313578

Standard Error 8.622489586

Observations 40

ANOVA

  df SS MS F Significance F

Regression 1 583.2793367 583.2793367 7.845330329 0.007969295

Residual 38 2825.198413 74.34732666

Total 39 3408.47775      

  Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 2.784537846 6.904341063 0.403302476 0.6889861 -11.19256979 16.76164548 -11.19256979 16.76164548

X Variable 1 0.10213525 0.036464481 2.800951683 0.007969295 0.028316768 0.175953733 0.028316768 0.175953733

i) Mean

ii) Standard Deviation, σ

For For

10 (a)

iii) Min and Max Value

10 (a)

10 (b)

100 150 200 250 300 350 4000

5

10

15

20

25

30

35

40

45

50

WEIGHT (LBS) Vs BODY FAT (%)

Body Fat (%), y

Linear (Body Fat (%), y)

WEIGHT (LBS)

BOD

Y FA

T (%

)

y = 0.1021x + 2.7911

R = 0.4137

10 (c)

So,

10 (d)

The hypothesis is rejected because F ₀ = 7.8421 is bigger than 4.08

10 (e)

Intercept = Slope =

From the regression line, the value of intercept is fixed and the vlue of slope can be changed whether increase or decrease depends on value of x. When weight (lbs), x is increased then the percent of body fat, y is also increase.

10 (f)

STEP 1:

State the hypothesis

(two tail test)

STEP 2:

STEP 3:

10 (f)

STEP 4:

Accept H0, since Ztest is more than Ztable.

10 (g)

Weight (lbs),    

Body Fat (%)

Body Fat (%),

Weight (lbs)

10 (h)

10 (i)

So,Coefficient of Pearson is below 0.5, so it is weak positive correlation.