Question $2$

The management of an office complex in central Johannesburg wants to understand the pattern of energy consumption $($i$.$e$.$ energy costs related to heating and air$-$conditioning$)$ in the complex. They have assembled quarterly data on energy costs for the past three years.

$\backslash$table$[[$Year$,$Season$],[$Summer$,$Autumn,Winter,Spring$],[2021,240000,380000,450000,310000],[2022,760000,910000,980000,820000],[2023,1260000,1450000,1500000,1330000]]$

Page $3$ of $5$

$2\mathrm{.}1.$ Plot the pattern of energy costs graphically. Comment.

$(8)$

$2\mathrm{.}2.$ Calculate seasonal indexes for the complex's energy costs and interpret the seasonal impact.

$(8)$

$2\mathrm{.}3.$ Find the least squares trendline for energy usage in this office complex.

$(10)$

$2\mathrm{.}4.$ How much should the financial manager of this office complex budget for energy costs for each quarter of $2024,$ based on seasonally adjusted trend estimates?

$(8)$