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
Calculate the predicted deseasonalised value for time period $15$15, to four decimal places.
If the seasonal index for this period was $77%$77%, calculate the true predicted value to four decimal places.
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.
No it is not as it is an extrapolation beyond the given data set.
No it is not as we do not know the value of the correlation coefficient.
No, it cannot be considered reliable as it is beyond one cycle of the original data.
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.
It has no meaning in this situation.
It indicates that there is an increasing trend as the gradient of the regression line is positive.
It's the value of $y$y when $t=0$t=0.
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
The petrol price cycle at a local service station is monitored. The results over two weeks are given in the table below.
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.