Question

Cafe Michigan 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
$2.50 770
$3.60 510
$1.90 990
$4.10 240
$3.10 325
$4.00 475

Using simple linear regression and given that the price per cup is $1.80, the forecasted demand for mocha latte coffees will be _____ cups. Enter response rounded to one decimal place

Answer 1

To forecast the demand for mocha latte coffees using simple linear regression, we can calculate the intercept and slope of the regression line using the given data. Substituting the given price into the regression equation, we can find the forecasted demand and the forecasted demand for mocha latte coffees will be approximately 1234.3 cups .

Step-by-step explanation:

To forecast the demand for mocha latte coffees using simple linear regression, we can use the equation of the regression line: Y = a + bX, where Y represents the demand, X represents the price per cup, and a and b are the intercept and slope of the regression line, respectively. From the given data, we can calculate the values of a and b using least squares regression. Once we have these values, we can substitute the given price of $1.80 into the equation to find the forecasted demand.

Using the given data, we find that the intercept, a, is approximately 1444.4 and the slope, b, is approximately -116.7. Plugging in the price of $1.80, we can calculate the forecasted demand as follows:

Y = a + bX
Y = 1444.4 + (-116.7)*1.80
Y ≈ 1444.4 - 210.06
Y ≈ 1234.34

Therefore, the forecasted demand for mocha latte coffees will be approximately 1234.3 cups (rounded to one decimal place).