The daily deseasonalised prices for a petrol outlet for a week (in cents/litre) are given in thefollowing table (where Sunday is day 1, Monday is day 2, etc). The equation of the least squares regression line that could enable us to predict thedeseasonalised price is closest to:

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The question asks for the least squares regression line that could be used to predict the deseasonalised price based on the day of the week (with Sunday as day 1, up to Saturday as day 7).

Option by option analysis:

Option a: deseasonalised price = 0.601 − 49.7 × day
- This gives a very small intercept and a large negative slope. Since the observed prices across the week show an overall increasing trend from Sunday (88.3) to Saturday (94.6), a steep negative slope would predict prices falling as day increases, which contradicts the data. Therefore this option is unlikely to fit the data well.

Option b: deseasonalised price = 84.3 − 1.25 × day
- Here the intercept is plausible (around the average price), but the slope is negative, implying prices decrease with later days. The actual data show prices rising across the week, so a negative slope misrepresents the trend and would not be a good fit.

Option c: deseasonalised price = 84.3 + 1.25 × day
- This option uses an intercept around the average price (84.3 cents/litre) and a positive slope (1.25 cents per day), which aligns with the observed upward trend from Sunday through Saturday (88.3 to 94.6). This shape matches the pattern in the table and typical least-squares behavior when prices increase over successive days.

Option d: deseasonalised price = 1.25 + 84.3 × day
- This form is illogical: it places the very large term 84.3 × day as the dominant component, which would predict astronomically large prices as day increases, certainly not consistent with the data. Additionally, the intercept is not presented in a compatible form for typical regression models here.

Overall reasoning: Among the given options, the one with a plausible intercept near the average price and a small positive slope that mirrors the increasing prices over the week best matches the data pattern. The data show a rising trend from Sunday to Saturday, so a positive slope is appropriate, and the intercept around 84.3 cents aligns with the central tendency of the prices. The option with a negative slope contradicts the observed trend, and the options with implausible or nonsensical coefficients do not fit the regression framework here.

MUF0142 Fund. Mathematics Unit 2 - Semester 1, 2025 9.4 Time Series: Seasonality Quiz (Formative)

The daily deseasonalised prices for a petrol outlet for a week (in cents/litre) are given in thefollowing table (where Sunday is day 1, Monday is day 2, etc). The equation of the least squares regression line that could enable us to predict thedeseasonalised price is closest to:

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