Answer:
The demand for mocha latte coffee should be 900.6 cups at the price of $1.85 forecast developed on the basis of linear regression model
Explanation:
Price, here is the independent variable i.e., X and Demand (Y) is a dependent variable. The simple linear regression is Y = a + bX
Since we need to find the value of intercept ‘a’ and slope ‘b’, we need to have two equations to find these two values. These two equations are
Σy = na+ bΣX
ΣXY = aΣX + bΣX^2
We can see that ΣX = 19.1, ΣY = 3295, ΣX^2 = 64.63 and ΣXY = 9480.5
(For the calculation of the values provided above values consult the word document attached)
Plugging in the values into the equations, we get
3295 = 6a +19.1b equation (i)
9480 = 19.1a +64.63b equation (ii)
To solve the equations we multiply the equation (i) by 19.1 and equation (ii) by 6, we get
62,934.5= 114.6a + 364.81b equation (i)
56,880= 114.6a + 387.78b equation (ii)
Subtracting equation (ii) from equation (i), we get
6054.5 = –22.97b
b = –263.58
Plugging the value of b in equation (i) we get
3295 = 6a +(–263.58 × 19.1)
3295 = 6a – 5,034.38
a = 1388.23
Having known the value of the intercept, we can forecast the demand for coffee at $1.85 as under
Y = 1388.23 + (–263.58 ×1.85)
Y = 900.6 approximately
