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5.05 Making predictions using time series data

Interactive practice questions

Data following a $5$5 point cyclical pattern is collected and seasonally adjusted for time periods $1$1 to $14$14. A least squares regression line is fitted to seasonally adjusted data, which appears linear, and is given by:

$y=2.4378t+66.2925$y=2.4378t+66.2925

a

Calculate the predicted deseasonalised value for time period $15$15, to four decimal places.

b

If the seasonal index for this period was $77%$77%, calculate the true predicted value to four decimal places.

c

Is this true predicted value considered reliable?

Yes, although it is an extrapolation it can be considered reliable as it is within one cycle of the original data.

A

No it is not as it is an extrapolation beyond the given data set.

B

No it is not as we do not know the value of the correlation coefficient.

C

No, it cannot be considered reliable as it is beyond one cycle of the original data.

D
d

What is the meaning of the coefficient in front of $t$t in the least squares regression line?

It indicates that there is a decreasing trend as the gradient of the regression line is negative.

A

It has no meaning in this situation.

B

It indicates that there is an increasing trend as the gradient of the regression line is positive.

C

It's the value of $y$y when $t=0$t=0.

D
Easy
4min

Data following a $3$3 point cyclical pattern is collected and seasonally adjusted for time periods $1$1 to $12$12. A least squares regression line is fitted to the seasonally adjusted data and is given by:

$y=-2.1404t+51.4172$y=2.1404t+51.4172

Easy
2min

The petrol price cycle at a local service station is monitored. The results over two weeks are given in the table below.

Medium
10min

A new pop up ice-cream shop records their sales over their first month. The data is tabulated below.

Note that the shop is only open over the weekend.

Medium
10min
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Outcomes

4.1.6

fit a least-squares line to model long-term trends in time series data

4.1.7

predict from regression lines, making seasonal adjustments for periodic data

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