Question

1) What is the value of b1? X: 12, 21, 28, 8, 20. Y: 17, 15, 22, 19, 24

2) What is the value of b0? X: 12, 21, 28, 8, 20. Y: 17, 15, 22, 19, 24

3) What is the equation of the y-hat estimator line? X: 12, 21, 28, 8, 20. Y: 17, 15, 22, 19, 24.

a. Y=0.162-16.51x b. y=0.162+16.51x c. Y=16.51-0.162x d. Y=16.51+0.162x

4) If x is increased by 10 units, how much does y-hat change?

5) Assume b0=12.953, and b1=-2.5. For x=25, predict y.

6) How much correlation is there between x and y? X: 12, 21, 28, 8, 20. Y: 17,15, 22, 19, 24.

7) How much of the variability in y is explained by x? X: 12, 21, 28, 8, 20. Y: 17, 15, 22, 19, 24.

8) Executives of a video rental chain want to predict the success o a potential new store. The company's researcher beings by gathering information on number o rentals and average family income from several of the chain's present outlets. The results of that effort are available in the attached data file.

rentals: 710, 529, 314, 504, 619, 428, 317, 205, 468, 545, 607, 694.  

Average family income ($1,000): 65, 43, 29, 47, 52, 50, 46, 29, 31, 43, 49, 64

a. y=10.626+9.729x b. y=9.729+10.626x c. y=10.626-9.729x d. y=-9.729-10.626x

9) Following Question 8, How much correlation exists between x and y?

10)Following question 8, How much of the variation in y is accounted for by x?

Answer 1

(1,2,3 are included in this explanation )

Sum of X = 89
Sum of Y = 97
Mean X = 17.8
Mean Y = 19.4
Sum of squares (SS_X) = 248.8
Sum of products (SP) = 40.4

Regression Equation = ŷ = bX + a

b = SP/SS_X = 40.4/248.8 = 0.16238

a = M_Y - bM_X = 19.4 - (0.16*17.8) = 16.50965

Y = B0 +B1(X)

ŷ = 0.16238X + 16.50965 (equation)( option d of (3)

B0= 16.50965

B1= 0.16238

(5) Assume b0=12.953, and b1=-2.5. For x=25, predict y.

y =b0 +b1(x)

y=12.95+(-2.5)25= -49.55

(6) r = 0.3512

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