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:

Price Number Sold

$2.70 765

$3.60   510

$2.00 975

$4.10 245

$3.10 325

$4.05 475

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 $1.80? round to one decimal

Answer 1

Solution:
Simple regression equation can be calculated as
Y = a + bX
Here Y is dependent variable which is Number sold
X is independent variable which is Price
a is intercept of regression line
b is the slope of regression line
Slope of line can be calculated as
Slope = (n*summation(XY) - Summation(X)*Summation(Y)) / (n*Summation(X^2) - (Summation(X))^2)

Price(X)	Number Sold(Y)	X^2	Y^2	XY
2.7	765	7.29	585225	2065.5
3.6	510	12.96	260100	1836
2	975	4	950625	1950
4.10	245	16.81	60025	1004.5
3.10	325	9.61	105625	1007.5
4.05	475	16.4025	225625	1923.75
19.55	3295	67.0725	2187225	9787.25

Slope = (6*9787.25 - 19.55*3295)/(10*67.0725 - 19.55*19.55) = -281.4
Intercept can be calculated as = (Summation(Y) - Slope*Summation(X))/6 = (3295+281.4*19.55)/6 = 1466.1
So regression line is
Y = 1466.1 - 281.4*X
given in the question X= 1.80 So from regression equation, we can forecast to be sold mocha latte coffees
Y = 1466.1 - 281.4*1.80 = 959.56 or 959.6