Question

​Café Michigan's​ manager, Gary​ Stark, suspects that demand for mocha latte coffees depends on the price being charged. Based on historical​ observations, Gary has gathered the following​ data, which show the numbers of these coffees sold over six different price​ values:

Observation   Price   Number Sold
1   $2.60   770
2   $3.50   505
3   $2.00   975
4   $4.30   250
5   $3.20   320
6   $4.00   480

Using

simple linear regression

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and given that the price per cup is

​$1.75 the forecasted demand for mocha latte coffees will benothing cups ​(enter your response rounded to one decimal​ place).

Answer 1

	Price (x)	Number sold (y)	xy	x2
	2.6	770	2002	6.76
	3.5	505	1767.5	12.25
	2	975	1950	4
	4.3	250	1075	18.49
	3.2	320	1024	10.24
	4	480	1920	16
Total	19.6	3300	9738.5	67.74

x-bar = Sum(x)/n = 19.6/6 = 5.6
y-bar = Sum(y)/n = 3300/6 = 550

b = (Sum(xy) – n*x-bar*y-bar)/(Sum(x2) – n*x-bar*x-bar) = (9738.5-6*3.266666667*550)/(67.74– 6*3.266666667*3.266666667)
   = -1041.500001/3.71333332 = -280.4757643

a = y-bar –b*x-bar
= 550- (-280.4757643)*3.266666667 = 1466.22083

Regression equation is y = a + bx,
we get following regression equation by substituting values of a and b
Regression equation is y =1466.22083-280.4757643x

given that the price per cup is $1.75 the forecasted demand for mocha latte coffees will be 1466.22083-280.4757643*1.75 = 975.3882425 = 975.4 cups (Rounded to 1 decimal place)