- Stuart is investigating the relationship between Gross Domestic Product (GDP) and the size of the population for a particular country.
He takes a random sample of 9 years and records the size of the population, \(t\) millions, and the GDP, \(g\) billion dollars for each of these years.
The data are summarised as
$$n = 9 \quad \sum t = 7.87 \quad \sum g = 144.84 \quad \sum g ^ { 2 } = 3624.41 \quad S _ { t t } = 1.29 \quad S _ { t g } = 40.25$$
- Calculate the product moment correlation coefficient between \(t\) and \(g\)
- Give an interpretation of your product moment correlation coefficient.
- Find the equation of the least squares regression line of \(g\) on \(t\) in the form \(g = a + b t\)
- Give an interpretation of the value of \(b\) in your regression line.
- Use the regression line from part (c) to estimate the GDP, in billions of dollars, for a population of 7000000
- Comment on the reliability of your answer in part (i). Give a reason, in context, for your answer.
Using the regression line from part (c), Stuart estimates that for a population increase of \(x\) million there will be an increase of 0.1 billion dollars in GDP.
- Find the value of \(x\)