Question

v

Consider the monthly time series shown in the table.

Month	t	Y
January	1	185
February	2	192
March	3	189
April	4	201
May	5	195
June	6	199
July	7	206
August	8	203
September	9	208
October	10	209
November	11	218
December	12	216

1. Use the method of least squares to fit the model E(Yt) = β0 + β1t to the data. Write the prediction equation.
2. Use the prediction equation to obtain forecasts for the next two months.
3. Find 95% forecast intervals for the next two months.

Answer 1

The terms least squares and regression are used interchangeably. I have perforomed the regression analysis with 95% confidence and the output id attached in the below image

The Mode is E(Yt) = 2.730769 * t + 184

Question (b)

To get the sample for next two months substitute t as 13, 14 and get the respective E(Yt) values

For t =13

E(Y13) = 2.730769 * 13 + 184

= 219.5

= 220 rounded to 2 decimals

for t=14

E(Y14) = 2.730769 * 14 + 184

= 222.2307

= 222 rounded to zero decimals

Question (c)

THe forecasted values for nect 2 periods are 219.5 and 222

We have the Standard error from the Regression statistics as 3.223113

The forecast intervals are calculated by (forecasted value + (or) - Standard error)

So 95% forecast intervals for 13th month = (219.5 - 3.223113 , 219.5 + 3.223113)

= (216.276886, 222.7231)

= (216.28, 222.72) rounded to 2 decimals

So 95% forecast intervals for 14th month = (222.2307 - 3.223113 , 222.2307 + 3.223113)

= (219.007656, 225.4539)

= (219.01, 225.45) rounded to 2 decimals