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A study was conducted within a group of women aged between 35 and 45 years old to etermine if the amount of fat each consumed per day was related to their cholesterol c) levels (mg/) in blood. The data is shown below. Fat (gram) 50 65 45 29 38 53 72 31 Cholesterol level (mg/l) 175 210 190 100 165 199 230 145 i) Calculate the correlation coefficient and describe the relationship between the (7 marks) (6 marks) (2 marks) measured variables. ii) Derive the equation for regression line for the above data in 3c). il) Calculate the cholesterol level if 40 gram of fat is consumed.
math   Statistics-And-Probability   
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Answer #1

X = Fat

Y = Cholesterol level

X Y X.Y X.X Y.Y

50 65 45 29 38 53 72 31 175 210 190 100 165 199 230 145 8750 13650 8550 2900 6270 10547 16560 4495 2500 4225 2025 841 1444 2809 5184 961 30625 44100 36100 10000 27225 39601 52900 21025 Find the sum of every column to get: ΣΧ-383, ΣΥ-1414, ΣΧ. Υ.. 71722, ΣΧ2-19989, ΣΥ2-261576 Use the following formula to work out the correlation coefficient. 8-71722- 383 1414 0.9176 8-19989-38321 . 18 . 261576-14142

Strong positive correlation between Fat and Cholesterol level

ii)

5x-383 , y Y= 1414 , 5X-Y 71 722 , 5x2-19989 Use the following equations to find a and b: Σ Υ . Σ x?-Σχ . ΣΧΥ 1414 . 19989-383 . 71722 8.19989 - 3832 60.116 n.ΣΧΥΣΧ.ΣΥ 8.71722-383 . 1414 n.ΣΧ2-(ΣΧ)2 8-19989 (83) 2.450 8.19989-(383)2 Substitute a and b in regression equation formula y=a+b-z y 60.116 + 2.436-z

iii)

x = 40

y = 60.116 + 2.436 ( 40 )

y = 157.556

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