12 4. A researcher is investigating the relationship between elevation, x metres, and annual mean temperature, t °C. From a random sample of 20 weather stations in Switzerland, the following results were obtained Sxx = 8 820 655        Stt = 444.7        ∑x = 28 130        ∑t = 94.62 The product moment correlation coefficient for these data is found to be −0.959 (a) Interpret the value of this correlation coefficient. (1) (b) Show that the equation of the regression line of t on x can be written as t = 14.3 − 0.00681x (4) The random variable W represents the elevations of the weather stations in kilometres. (c) Write down the equation of the regression line of t on w for these 20 weather stations in the form t = a + bw (1) (d) Show that the residual sum of squares (RSS) for the model for t and x is 35.7 correct to one decimal place. (1) One of the weather stations in the sample had a recorded elevation of 1100 metres and an annual mean temperature of 1.4 °C (e) (i) Calculate this weather station’s contribution to the residual sum of squares. Give your answer as a percentage. (2) (ii) Comment on the data for this weather station in light of your answer to part (e)(i). (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________