Question

Consider the following time series: t sales 1 6 2 11 3 9 4 16 5 17 Use simple linear regression analysis with t as the predictor variable to find the parameters for the line that minimizes MSE for this time series. Enter the data into Excel and use Excel for your calculations. Enter the exact answers. a) y-intercept, b0 = -0.67 b) slope, b1 = 0.31 What is the MSE if this model is used to forecast sales for time periods 1-5? c) MSE = What is the forecast for time period t = 6?\

Answer 1

Check the explanation

Explanation:

Period, X Actual , Y

1 6

2 11

3 9

4 16

5 17

Y= intercept + slope*x

Answer a and b:

INTERCEPT(known Y's,known X's) Slope(known Y's,known X's)

3.7 2.7

Simple linear regression equation is

Forecast, Y= 3.7+ 2.7*x

Period, X Actual , Y linear Absolute squared

trend deviation= deviation=

Forecast, |Forecast - (absolute

Y= 3.7+ 2.7*x Actual| deviation)^2

1 6 6.40 0.4 0.2

2 11 9.10 1.9 3.6

3 9 11.80 2.8 7.8

4 16 14.50 1.5 2.3

5 17 17.20 0.2 0.0

6 19.90

2.78

MSE

Answer c: MSE= 2.78

Answer d: Forecast for x= 6= 19.90