Question

For 8 consecutive months, a factory manager recorded the number of

(x, in 00's) and the cost of their production (y, in $'000). the following table summarize the manager's data.


Number of Items, x: 18 36 45 22 13 33 10 53

pfoduction Cost, y: 39 55 60 45 35 50 32 75

(a) Plot the data on a scatter diagram.

(b) Find the least-squares regression equation y=a+ bx.

(c) Predict the production cost if the number of items produced is 2500.

Answer 1

The least square regression equation for the data is : y = 0.91x + 22.73. The production cost for 2500 items is $2297.73

Using the data given, we can plot the scatterplot using technology and the least square regression equation is given as :

• y = 0.91x + 22.73

The production cost if number of items produced is 2500 can be obtained by Substituting into the regression equation.

y = 0.91(2500) + 22.73

y = 2297.73

Hence, the production cost for 2500 items is 2297.73