2. Paul believes there is a relationship between the value and the floor size of a house. He takes a random sample of 20 houses and records the value, \(\pounds v\), and the floor size, \(s \mathrm {~m} ^ { 2 }\)
The data were coded using \(x = \frac { s - 50 } { 10 }\) and \(y = \frac { v } { 100000 }\) and the following statistics obtained.
$$\sum x = 441.5 , \quad \sum y = 59.8 , \quad \sum x ^ { 2 } = 11261.25 , \quad \sum y ^ { 2 } = 196.66 , \quad \sum x y = 1474.1$$
- Find the value of \(S _ { x y }\) and the value of \(S _ { x x }\)
- Find the equation of the least squares regression line of \(y\) on \(x\) in the form \(y = a + b x\)
The least squares regression line of \(v\) on \(s\) is \(v = c + d s\)
- Show that \(d = 1020\) to 3 significant figures and find the value of \(c\)
- Estimate the value of a house of floor size \(130 \mathrm {~m} ^ { 2 }\)
- Interpret the value \(d\)
Paul wants to increase the value of his house. He decides to add an extension to increase the floor size by \(31 \mathrm {~m} ^ { 2 }\)
- Estimate the increase in the value of Paul's house after adding the extension.