Question

The number of internal disk drives​ (in millions) made at a plant in Taiwan during the past 5 years​ follows:                                                                     Year 1 2 3 4 5 Disk Drives 138 160 196 200 210 ​a) Using simple linear regression LOADING... ​, the forecast for the number of disk drives to be made next year​ = nothing disk drives ​(round your response to one decimal​ place). ​b) The mean squared error​ (MSE) when using simple linear regression​ = nothing drives squared ​(round your response to one decimal​ place). ​c) The mean absolute percentage error​ (MAPE) when using simple linear regression​ = nothing ​% ​(round your response to one decimal​ place).

Answer 1

Year	Disk Drives
1	138
2	160
3	196
4	200
5	210

a.) Linear regression is of the form

y = a + b*x

First finding mean, standard devaition for both x and y we get

mx = 15/5 = 3

my = 904/5 = 180.8

sx = 1.58

sy = 30.482

Correlation between x and y is given as,

r = 0.954

So, b = r * (sy/sx)

b = 0.954 *(30.482/1.58)

b = 18.4

a = my - b*mx

a = 180.8 - 18.4 * 3

a = 125.58 = 125.6

So, equation becomes,

y(disk drive) = 125.6+ 18.4 * x(year)

b.)

Mean Squared Error = Sum of squared error / n

First predtcing values of y based on above equation,

Year	Disk Drives	Predicted	(Error)^2
1	138	144	36
2	160	162.4	5.76
3	196	180.8	231.04
4	200	199.2	0.64
5	210	217.6	57.76

Sum of squared error = 331.2

So, Mean Squared error = 331.2 / 5 = 66.24

c.)

If we multiply above by 100, we get percentage.

Year	Disk Drives	Predicted	|Actual - Predicted|	|Actual - Predicted| / Actual
1	138	144	6	0.0435
2	160	162.4	2.4	0.0150
3	196	180.8	15.2	0.0776
4	200	199.2	0.8	0.0040
5	210	217.6	7.6	0.0362

Sum of Last column = 0.1762

So, MAPE = (0.1762/5) * 100

MAPE = 3.524