8 An estate agent collects data for a random selection of 13 flats in order to investigate the link between the floor areas of flats and their price. The scatter diagram shows the floor areas, \(x \mathrm {~m} ^ { 2 }\), and prices, \(\pounds y\) thousand, of the 13 flats.
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- The estate agent notes that two of the data points are outliers. One is Flat A which has a large floor area but is in poor condition. The other is Flat B which has a balcony with a desirable view overlooking the sea.
Label these two data points on the copy of the scatter diagram in the Printed Answer Booklet.
The estate agent decides to remove these two data points from the analysis. Summary statistics for the remaining 11 flats are as follows.
$$\sum x = 652.5 \quad \sum y = 5067 \quad \sum x ^ { 2 } = 41987.35 \quad \sum y ^ { 2 } = 2456813 \quad \sum x y = 315928.2$$
- In this question you must show detailed reasoning.
Calculate the equation of a regression line which is suitable for estimating the price of a flat from its floor area.
- Use the regression line to estimate the price for the following floor areas.
- \(40 \mathrm {~m} ^ { 2 }\)
- \(110 \mathrm {~m} ^ { 2 }\)
- Given that the value of the product moment correlation coefficient for these 11 data items is 0.765 , comment on the reliability of your estimates.
- The estate agent thinks that he can predict the floor area of a flat from its price, using the equation of the regression line found in part (b).
Comment briefly on the estate agent's idea.