SSCE HSC Mathematics Standard Annuities: A university uses gas to heat it

Question

A university uses gas to heat its buildings. Over a period of 10 weekdays during winter, the gas used each day was measured in megawatts (MW) and the average outside temperature each day was recorded in degrees Celsius (°C).

Using $x$ as the average daily outside temperature and $y$ as the total daily gas usage, the equation of the least-squares regression line was found.

The equation of the regression line predicts that when the temperature is 0°C, the daily gas usage is 236 MW.

The ten temperatures measured were: 0°, 0°, 2°, 5°, 7°, 8°, 9°, 9°, 10°.

The total gas usage for the ten weekdays was 1840 MW.

In any bivariate dataset, the least-squares regression line passes through the point $(\bar{x}, \bar{y})$, where $\bar{x}$ is the sample mean of the $x$-values and $\bar{y}$ is the sample mean of the $y$-values.

(a) Using the information provided, plot the point $(\bar{x}, \bar{y})$ and the $y$-intercept of the least-squares regression line on the grid.

A university uses gas to heat its buildings - HSC - SSCE Mathematics Standard - Question 34 - 2023 - Paper 1

Worked Solution & Example Answer:A university uses gas to heat its buildings - HSC - SSCE Mathematics Standard - Question 34 - 2023 - Paper 1

Calculate $\bar{x}$ and $\bar{y}$

Plot the point $(\bar{x}, \bar{y})$

Find the $y$-intercept of the regression line

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