Café Michigan\'s manager, Gary Stark, suspects that demand for mocha latte coffe
ID: 3040140 • Letter: C
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
760
$3.60
515
$1.90
975
$4.20
240
$3.10
325
$4.05
475
Using simple linear regression and given that the price per cup is $1.75, the forecasted demand for mocha latte coffees will be __ cups (enter your response rounded to one decimal place).
Explanation / Answer
Using R software
Let X be the Price per cup
Y be the Number Sold
Fitting Regression of Y on X
Results:
> x=c(2.7,3.6,1.9,4.2,3.1,4.05)
> y=c(760,515,975,240,325,475)
> lm(y~x)
Call:
lm(formula = y ~ x)
Coefficients:
(Intercept) x
1422.0 -268.1
>
Regression Eqution
Y= 1422 – 268.1(X)
For Price = $1.75
X=1.75
Y= 1422 – 268.1(1.75)
= 952.825
Demand is nearly 953