- Two economics students, Andi and Behrouz, are studying some data relating to unemployment, \(x \%\), and increase in wages, \(y \%\), for a European country. The least squares regression line of \(y\) on \(x\) has equation
$$y = 3.684 - 0.3242 x$$
and
$$\sum y = 23.7 \quad \sum y ^ { 2 } = 42.63 \quad \sum x ^ { 2 } = 756.81 \quad n = 16$$
- Show that \(\mathrm { S } _ { y y } = 7.524375\)
- Find \(\mathrm { S } _ { x x }\)
- Find the product moment correlation coefficient between \(x\) and \(y\).
Behrouz claims that, assuming the model is valid, the data show that when unemployment is 2\% wages increase at over 3\%
- Explain how Behrouz could have come to this conclusion.
Andi uses the formula
$$\text { range } = \text { mean } \pm 3 \times \text { standard deviation }$$
to estimate the range of values for \(x\).
- Find estimates of the minimum value and the maximum value of \(x\) in these data using Andi's formula.
- Comment, giving a reason, on the reliability of Behrouz's claim.
Andi suggests using the regression line with equation \(y = 3.684 - 0.3242 x\) to estimate unemployment when wages are increasing at \(2 \%\)
- Comment, giving a reason, on Andi's suggestion.
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