A large company rents shops in different parts of the country. A random sample of 10 shops was taken and the floor area, $$\(x\)$$ in $$\(10 \mathrm{~m}^{2}\)$$, and the annual rent, $$\(y\)$$ in thousands of dollars, were recorded. The data are summarised by the following statistics $$\[ \sum x=900 \quad \sum x^{2}=84818 \quad \sum y=183 \quad \sum y^{2}=3434 \]$$ and the regression line of $$\(y\)$$ on $$\(x\)$$ has equation $$\(y=6.066+0.136 x\)$$ (a) Use the regression line to estimate the annual rent in dollars for a shop with a floor area of $$\(800 \mathrm{~m}^{2}\)$$ (2) (b) Find $$\(\mathrm{S}_{y y}\)$$ and $$\(\mathrm{S}_{x x}\)$$ (3) (c) Find the product moment correlation coefficient between $$\(y\)$$ and $$\(x\)$$. (4) An 11th shop is added to the sample. The floor area is $$\(900 \mathrm{~m}^{2}\)$$ and the annual rent is 15000 dollars. (d) Use the formula $$\(\mathrm{S}_{x y}=\sum(x-\bar{x})(y-\bar{y})\)$$ to show that the value of $$\(\mathrm{S}_{x y}\)$$ for the 11 shops will be the same as it was for the original 10 shops. (2) (e) Find the new equation of the regression line of $$\(y\)$$ on $$\(x\)$$ for the 11 shops. (3) The company is considering renting a larger shop with area of $$\(3000 \mathrm{~m}^{2}\)$$ (f) Comment on the suitability of using the new regression line to estimate the annual rent. Give a reason for your answer. (1)

Answer:

Knowledge points:

Solution: