Question

24. United Widget Manufacturing has a problem with defective widgets. Employees make hundreds of thousands of them each day, and many are defective. United has instituted training for the workers, and you would like to predict the number of defects per week based on the number of days of training an employee has received. You obtain the following data: Employee number 1015 2023 1153 4029 1117 0012 Days of training 4 5 6 4 3 2 Defects per week (100's) 19 17 7 14 22 23 (a) Determine the regression equation. Answer: (b) Interpret the meaning of the slope using the words of the problem.

Answer 1

Answers:

a)
X Y Χ.Υ Χ. Χ 4 19 76 16 5 17 85 25 6 7 42 36 4 14 56 16 3 22 66 9 2 23 46 4 Step 2: Find the sum of every column: ΣΧ = 24, ΣΥ = 102, ΣΧ. Υ = 371, Σx? = 106

Step 3: Use the following equations to find a and b: α - ΣΥΣΧ2 – ΣΧΣΧΥ η· ΣΧ2 – (ΣΧ)? 102 - 106 – 24 - 371 6. 106 – 242 Ν 31.8 b η-ΣΧΥ – ΣΧ.ΣΥ η·Σ Χ2 – (ΣΧ)? 6. 371 – 24. 102 6. 106 – (24)? N -3.7 Step 4: Substitute a and b in regression equation formula y = α + 6.0 y = 31.8 3.7 .α
Therefore, regression equation is Y = 31.8-3.7X

b) For every one unit increase in number of days of training, defects per week will decrease by 3.7 (1000's)

c) If X = 6,

Y = 31.8-(3.7*6) = 9.6

Therefore, number of defects per week is 9.6( 1000's), for an employee who has 6 days of training

d) coefficient of determination = R2

Step 2: Find the sum of every column to get: ΣΧ = 24, ΣΥ = 102, ΣΧ.Υ = 371, ΣΧ? = 106, ΣΥ? = 1908 Step 3: Use the following formula to work out the correlation coefficient. η·ΣΧΥ – ΣΧ.ΣΥ r [n ΣΧ2 - (ΣΑ)?] : [n ΣΥ? – (ΣΥ)?] 6. 371 – 24 - 102 Υ - & – 0.887 [6 - 106 – 24?] - [6 - 1908 – 1022)

= (-0.887)*(-0.887) =0.7868= 78.68%

78.68% of data fits the regression model,it indicates better fit of the model