Means from a regression line through the mean point, a missing data value and the correlation coefficient
Means from a regression line through the mean point, a missing data value and the correlation coefficient
7 marks
On eight days a café recorded the number of hours of sunshine, \(x\), and its takings from cold drinks, \(y\) hundred dollars. The results are shown in the table, where one value of \(y\) has been replaced by \(p\).
| \(x\) | \(3.9\) | \(2.0\) | \(4.9\) | \(5.6\) | \(8.1\) | \(5.4\) | \(5.3\) | \(4.8\) |
|---|---|---|---|---|---|---|---|---|
| \(y\) | \(11.8\) | \(6.6\) | \(14.1\) | \(14.8\) | \(18.9\) | \(p\) | \(12.6\) | \(11.5\) |
- Find the mean number of hours of sunshine, \(\bar{x}\).[2]
For these data, the equation of the regression line of \(y\) on \(x\) is \(y=1.9375x+3.1375\).
- Find
- \(\bar{y}\)
- \(p\).[4]
- Hence, find the value of Pearson's product-moment correlation coefficient, \(r\), for these data.[1]
Solution:
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Answer:(a) \(\bar{x}=5\) (b)(i) \(\bar{y}=12.825\) (b)(ii) \(p=12.3\) (c) \(r=0.955\)
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