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, $$\(t\)$$ millions, and the GDP, $$\(g\)$$ billion dollars for each of these years. The data are summarised as $$\[ n=9 \quad \sum t=7.87 \quad \sum g=144.84 \quad \sum g^{2}=3624.41 \quad S_{t t}=1.29 \quad S_{t g}=40.25 \]$$ (a) Calculate the product moment correlation coefficient between $$\(t\)$$ and $$\(g\)$$ (3) (b) Give an interpretation of your product moment correlation coefficient. (1) (c) Find the equation of the least squares regression line of $$\(g\)$$ on $$\(t\)$$ in the form $$\(g=a+b t\)$$ (4) (d) Give an interpretation of the value of $$\(b\)$$ in your regression line. (1) (e) (i) Use the regression line from part (c) to estimate the GDP, in billions of dollars, for a population of 7000000 (2) (ii) Comment on the reliability of your answer in part (i). Give a reason, in context, for your answer. (1) Using the regression line from part (c), Stuart estimates that for a population increase of $$\(x\)$$ million there will be an increase of 0.1 billion dollars in GDP. (f) Find the value of $$\(x\)$$ (2)

Answer:

Knowledge points:

Solution: