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 $2.50 760 $3.60 515 $1.90 980 $4.10 245 $3.00 320 $4.00 475 Using simple linear regressionLOADING... and given that the price per cup is $1.85, the forecasted demand for mocha latte coffees will be nothing cups (enter your response rounded to one decimal place).

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

how does that happen,where u steel points

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