Question

Using the data in the table​ below, estimate the demand function for cod.

                                                                                                                         

​Price, dollars per pound	​Quantity, thousand pounds per day
1.90	1.5
1.35	2.2
1.25	4.4
1.20	5.9
0.95	6.5
0.85	7.0
0.73	8.8

Using the Excel trendline option to estimate a linear demand​ function, the linear demand function is

Qequals=12.53 minus 6.25 p12.53−6.25p.

Suppose the quantity in the first row of the table were

22

instead of 1.5.

The linear demand function would now be

Qequals=nothingminus−nothingp.

​(Enter your responses rounded to two decimal​ places.)

Answer 1

The linear trend line Regression Equation is represented by the following equation

y = a + b *x…………………….. (1)

Where a is the y-intercept of the line and b is the slope of the line.

Formula to calculate the a and b are following

Slop b = Sum of {(x-xbar)*(y-ybar)}/ Sum of {(x-xbar)^2}

Intercept a = ybar - b * x bar

	Price (x)	Quantity, thousand pounds per day (Y)	x - x bar	y - y bar	(x-xbar)*(y-ybar)	(x-xbar)^2	(y-ybar)^2
	1.90	1.5	0.72	-3.69	-2.67	0.52	13.58
	1.35	2.2	0.17	-2.99	-0.52	0.03	8.91
	1.25	4.4	0.07	-0.79	-0.06	0.01	0.62
	1.20	5.9	0.02	0.71	0.02	0.00	0.51
	0.95	6.5	-0.23	1.31	-0.30	0.05	1.73
	0.85	7.0	-0.33	1.81	-0.59	0.11	3.29
	0.73	8.8	-0.45	3.61	-1.61	0.20	13.06
Mean	1.18	5.19
	x bar ↑	ybar ↑
Sum					-5.73	0.92	41.71
		slop b = Sum of {(x-xbar)*(y-ybar)}/ Sum of {(x-xbar)^2}	-6.25
		Intercept a = ybar - b * x bar	12.53
	The linear Equation	Y = a + bx =	12.53- 6.25*x

Note: x is equal to p & y is equal to Q

Suppose the quantity in the first row of the table were 22 instead of 1.5.

	Price (x)	Quantity, thousand pounds per day (Y)	x - x bar	y - y bar	(x-xbar)*(y-ybar)	(x-xbar)^2	(y-ybar)^2
	1.90	22	0.72	13.89	10.06	0.52	192.81
	1.35	2.2	0.17	-5.91	-1.03	0.03	34.98
	1.25	4.4	0.07	-3.71	-0.28	0.01	13.80
	1.20	5.9	0.02	-2.21	-0.05	0.00	4.90
	0.95	6.5	-0.23	-1.61	0.36	0.05	2.61
	0.85	7.0	-0.33	-1.11	0.36	0.11	1.24
	0.73	8.8	-0.45	0.69	-0.31	0.20	0.47
Mean	1.18	8.11
	x bar ↑	ybar ↑
Sum					9.12	0.92	250.81
		slop b = Sum of {(x-xbar)*(y-ybar)}/ Sum of {(x-xbar)^2}	9.95
		Intercept a = ybar - b * x bar	-3.58
	The linear Equation	Y = a + bx =	9.95*x -3.58