Café Michigan’s manager, Gary Stark, suspects that demand for mocha latter coffe
ID: 446155 • Letter: C
Question
Café Michigan’s manager, Gary Stark, suspects that demand for mocha latter 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 Numbers Sold
$2.50 760
$3.40 510
$1.90 980
$4.30 245
$3.20 325
$4.10 490
Using simple linear regression and given that the price per cup is $1.80, the forecast demand for mocha latter coffees will be ______cups (enter your response rounded to one decimal place.)
Price Numbers Sold
Explanation / Answer
b = (NXY - (X)(Y)) / (NX2 - (X)2)
= ((6 * 9598.5) - (19.4 * 3310) / ((6 * 66.96) - (19.4)^2)
= -260.748 = -261
a = (Y - b(X)) / N
= (3310 - (-260 * 19.4)) / 6
= 1394.752
Y = a + bX
when X = 1.80, We get
Y = 1394.752 - (260.748 * 1.80) = 925.405
Using simple linear regression and the price per cup $1.80, the forecast demand for mocha latter coffees will be 925.4 cups.
Price (X) Unit Sold (Y) X^2 Y^2 X*Y 2.5 760 6.25 577600 1900 3.4 510 11.56 260100 1734 1.9 980 3.61 960400 1862 4.3 245 18.49 60025 1053.5 3.2 325 10.24 105625 1040 4.1 490 16.81 240100 2009 Sum 19.4 3310 66.96 2203850 9598.5