3. A company that manufactures spare parts experiences fluctuations in the lot s

Question

3. A company that manufactures spare parts experiences fluctuations in the lot sizes due to fluctuations in supply and demand. The company is interested in examining the relationship between the number of man-hours worked and lot size. The number of man-hours worked is taken as the dependent variable, where each (X, Y), combination represents one production run. Using the data below, answer the following questions X: 30 20 60 80 40 50 60 30 70 60 Y 73 50 128 170 87 108 135 69 148 132 a) Find the correlation coefficient between these two variables. Show your work. (b) Find the equation of the least square line for these data of determination in the context of the problem (d) Use the equation of the fitted line to predict the number of man hours worked when the lot size is set at 55

Explanation / Answer

Ans:

a)

Correlation cofficient,r:

r=(10*61800-500*1100)/SQRT((10*28400-500^2)*(10*134660-1100^2))=0.998

b)

Regression Equation(y) = a + bx
Slope(b) = (NXY - (X)(Y)) / (NX2 - (X)2)
Intercept(a) = (Y - b(X)) / N

slope,b=(10*61800-500*1100)/(10*28400-500^2)=2

y-intercept,a=(1100-2*500)/10=10

y'=10+2x

c)Cofficient of determination,r2=0.9982=0.996

It indicates that 99.6% of the linear variation of dependent variable,y(man hrs) is explained by the independent variable x(lot size)

d)when x=55

y=10+2*55=10+110=120

x y xy x^2 y^2 1 30 73 2190 900 5329 2 20 50 1000 400 2500 3 60 128 7680 3600 16384 4 80 170 13600 6400 28900 5 40 87 3480 1600 7569 6 50 108 5400 2500 11664 7 60 135 8100 3600 18225 8 30 69 2070 900 4761 9 70 148 10360 4900 21904 10 60 132 7920 3600 17424 Total= 500 1100 61800 28400 134660

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