The data below show consumption of margarine (in ounces per person per week) and its real price, for the UK.

(a) Draw an XY plot of the data and comment.

(b) From the chart, would you expect the line of best fit to slope up or down? In theory, which way should it slope?

(c) What would you expect the correlation coefficient to be, approximately?

(d) Calculate the correlation coefficient between margarine consumption and its price.

(e) Is the coefficient significantly different from zero? What is the implication of the result?

(The following totals will reduce the burden of calculation: ΣY = 67.52; ΣX = 2101.70; ΣY² = 245.055; ΣX² = 240 149.27; ΣXY = 7299.638; Y is consumption, X is price. If you wish, you could calculate a logarithmic correlation. The relevant totals are: Σy = 23.88; Σx = 89.09; Σy² = 30.45; Σx² = 418.40; Σxy = 111.50, where y = lnY and x = lnX.) 

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Year Consumption Price Year Consumption Price 1970 2.86 125.6 1980 3.83 104.2 1971 3.15 132.9 1981 4.11 95.5 1972 3.52 126.0 1982 4.33 88.1 1973 3.03 119.6 1983 4.08 88.9 1974 2.60 138.8 1984 4.08 97.3 1975 2.60 141.0 1985 3.76 100.0 1976 3.06 122.3 1986 4.10 86.7 1977 3.48 132.7 1987 3.98 79.8 1978 3.54 126.7 1988 3.78 79.9 1979 3.63 115.7