- Sammy is studying the number of units of gas, \(g\), and the number of units of electricity, \(e\), used in her house each week. A random sample of 10 weeks use was recorded and the data for each week were coded so that \(x = \frac { g - 60 } { 4 }\) and \(y = \frac { e } { 10 }\). The results for the coded data are summarised below
$$\sum x = 48.0 \quad \sum y = 58.0 \quad \mathrm {~S} _ { x x } = 312.1 \quad \mathrm {~S} _ { y y } = 2.10 \quad \mathrm {~S} _ { x y } = 18.35$$
- Find the equation of the regression line of \(y\) on \(x\) in the form \(y = a + b x\).
Give the values of \(a\) and \(b\) correct to 3 significant figures.
- Hence find the equation of the regression line of \(e\) on \(g\) in the form \(e = c + d g\).
Give the values of \(c\) and \(d\) correct to 2 significant figures.
- Use your regression equation to estimate the number of units of electricity used in a week when 100 units of gas were used.
（a）Find the probability distribution of \(X\) ．
（b）Write down the value of \(\mathrm { F } ( 1.8 )\) ．
（a）Find the probability distribution of \(X\) ．勤