Question

The Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. The bivariate data given below were taken from a sample of fifteen Cadets, each bought "new" two years ago and each sold "used" within the past month. For each Cadet in the sample, we have listed both the mileage, X (in thousands of miles), that the Cadet had on its odometer at the time it was sold used, and the price, y (in thousands of dollars), at which the Cadet was sold used. These data are shown graphically in the scatter plot in Figure 1. Also given are the products of the mileages and used selling prices for each of the fifteen Cadets. (These products, written in the column labelled "xy," may aid in calculations.) Mileage, x (in thousands) xy Used selling price, (in thousands of dollars) 27.6 31.3 28.3 803.16 845.1 665.05 696.71 26.9 25.5 31.2 711.45 714.48 732.55 29.9 29.1 27.0 23.5 25.9 27.9 22.9 24.5 20.7 24.3 23.2 20.8 27.7 15.3 37.4 34.3 31.0 641.7 27.4 33.3 31.3 29.9 34.5 23.1 26.2 665.82 772.56 651.04 828.23 527.85 863.94 898.66 Figure 1 Answer the following. Carry your intermediate computations to at least four decimal places, and round your answer as specified below. (If necessary, consult a list of formulas.) What is the value of the sample correlation coefficient for these data? Round your answer to at least three decimal places

Answer 1

The statistical software output for this problem is:

Simple linear regression results: Dependent Variable: y Independent Variable: x y = 41.200564 - 0.46972293 x Sample size: 15 R (correlation coefficient) = -0.82492872 R-sq = 0.68050739 Estimate of error standard deviation: 1.8128022

Hence,

Sample correlation coefficient = -0.825