Question

Coffee Palace's manager, Joe Felan, suspects that and for mocha latte coffees depends on the price being charged. Based on historical observations, Joe has gathered the following data, which show the numbers of these coffees sold over six different price values: 

Price	Number Sold
$2.70	760
$3.50	510
$2.00	980
$4.20	250
$3.10	320
$4.05	480

Using these data, how many mocha latte coffees would be forecast to be sold according to simple linear regression if the price per cup were $2.80?

Answer 1

Answer 2

The 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)	Number sold (y)	x - x bar	y - y bar	(x-xbar)*(y-ybar)	(x-xbar)^2	(y-ybar)^2
	2.70	760	-0.56	210.00	-117.25	0.31	44100.00
	3.50	510	0.24	-40.00	-9.67	0.06	1600.00
	2.00	980	-1.26	430.00	-541.08	1.58	184900.00
	4.20	250	0.94	-300.00	-282.50	0.89	90000.00
	3.10	320	-0.16	-230.00	36.42	0.03	52900.00
	4.05	480	0.79	-70.00	-55.42	0.63	4900.00
Mean	3.26	550.00
	x bar ↑	ybar ↑
Sum					-969.50	3.49	378400.00
		slop b = Sum of {(x-xbar)*(y-ybar)}/ Sum of {(x-xbar)^2}	-277.63
		Intercept a = ybar - b * x bar	1454.60
	The least square estimated Regression Equation	Y = a + bx =	1454.60- 277.63*x
	If x = $2.80	Y =1454.60- 277.63*2.80	677.25

By putting the value of a & b in equation (1), we get

The least square estimated Regression Equation    

Y = a + bx = 1454.60 + (-277.63) *x

If x = $2.80; then

Y = 1454.60 – 277.63 * 2.80 = 677.25

If the price per cup is $2.80 then 677.25 would be forecasted to be sold.