Question

QUESTION 4 The production department of NDB Electronics wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. The complete set of paired observations follows: Number of Assemblers (x) 2 5 8 11 14 18 One-Hour Production (units) () 18 25 32 50 80 (a) Find the equation of the least squares regression line Predict the production when the number of assemblers is 15 (c) Compute the Product Moment Correlation Coefficient (t) and interpret your answer (d) Compute the coefficient of determination and interpret your answer.

Please write clearly

Answer 1

a.

Y-M X-M₃ -7.6667 -4.6667 -1.6667 1.3333 4.3333 8.3333 (X-Mx)2 58.7778 21.7778 2.7778 1.7778 18.7778 69.4444 (X-MXXY-M) 230 79.3333 16.6667 SS: 173.3333 SP: 762

Sum of X = 58
Sum of Y = 210
Mean X = 9.6667
Mean Y = 35
Sum of squares (SS_X) = 173.3333
Sum of products (SP) = 762

Regression Equation = ŷ = bX + a

b = SP/SS_X = 762/173.33 = 4.3962

a = M_Y - bM_X = 35 - (4.4*9.67) = -7.4962

ŷ = 4.3962X - 7.4962

b. For x=15,

ŷ = (4.3962*15) - 7.4962=58.4468

c.

X - My Y - My -7.667 -4.667 -1.667 www o o o -30.000 - 17.000 - 10.000 -3.000 15.000 45.000 (X-M.)2 58.778 21.778 2.778 1.778 18.778 69.444 (Y-M.)2 900.000 289.000 100.000 9.000 225.000 2025.000 (X-MX)(Y-M) 230.000 79.333 16.667 -4.000 65.000 375.000 Mx: 9.667 My: 35.000 Sum: 173.333 Sum: 3548.000 Sum: 762.000

X Values
∑ = 58
Mean = 9.667
∑(X - M_x)² = SS_x = 173.333

Y Values
∑ = 210
Mean = 35
∑(Y - M_y)² = SS_y = 3548

X and Y Combined
N = 6
∑(X - M_x)(Y - M_y) = 762

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 762 / √((173.333)(3548)) = 0.9717

As r is near 1 and it is positive

So there is strong positive correlation between x and y

d. Here r=0.9717, so r^2=0.9717^2=0.9442

Hence 94.42% of variation in y is explained by x