Question

The marketing manager of the Mount Pleasant We vount Pleasant Seafood would like to determine the effect of price per pound on the sales of locally caught shrimp. Experimenting with price produced the rom data: PRICE PER POUND (DOLLARS) AVERAGE SOLD DAILY (NUMBER OF POUND) 200 190 188 180 II 6.00 6.50 6.75 7.00 7.25 7.50 8.00 8.25 8.50 8.75 9.00 170 162 160 155 156 140 133 USE ANSWER SHEET PROVIDED FOR THESE QUESTIONS. Assume a plot of Y versus X yielded an apparent linear relationship (NO NEED TO PLOT POINTS) Compute the regression coefficients (a and b). Interpret the slope (b) in this problem. b.

Answer 1

a)

Linear regression forecast Y = a + bx where h n(Exy) - (Ex)(y) n(Exº) - (Ex)2 Ey – bEx - A orj - bx Yc = Computed value of dependent variable x = Predictor (independent) variable b = Slope of the line a = Value of y, when x = 0

x	y	x*y	x*x	y*y
6.00	200	1,200	36.00	40,000.0
6.50	190	1,235	42.25	36,100.0
6.75	188	1,269	45.56	35,344.0
7.00	180	1,260	49.00	32,400.0
7.25	170	1,233	52.56	28,900.0
7.50	162	1,215	56.25	26,244.0
8.00	160	1,280	64.00	25,600.0
8.25	155	1,279	68.06	24,025.0
8.50	156	1,326	72.25	24,336.0
8.75	140	1,225	76.56	19,600.0
9.00	133	1,197	81.00	17,689.0
84	1,834.00	13,718.25	643.50	310,238.00

n	11.00
n*Sum(xy)	150,900.75
Sumx*Sumy	153,139.00
n*sumx2	7,078.50
(Sumx)2	6,972.25

b = (150900.75 - 153139)/(7078.50 - 6972.25) = -21.066

a = (1834 - 21.066*84)/11 = 326.636

b) The slope is -21.066 which is negative. It means that with increase in the value of x (Price per pound), the y (average sold quantity) goes down