Question

Here is a bivariate data set. х у 91.1 82.3 94.3 43.6 72.7 6.3 89.5 -19.9 73.8 141 85.8 76.9 48 -92.1 69 177 69.2 -34.7 90.1 130.2 102.2 245.2 74 101.2 81.9 -24 94 -23.8 51 -2.6 Find the correlation coefficient and report it accurate to three decimal places. What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. %

Answer 1

The statistical software output for this problem is :

Simple linear regression results: Dependent Variable: y Independent Variable: x y=-147.55654 +2.545043 x Sample size: 15 R (correlation coefficient) = 0.43062342 R-sq-0.18543653 Estimate of error standard deviation: 87.077386 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -147.55654 119.17123 +0 13 -1.2381893 0.2375 Slope 2.545043 1.4794091 +0 13 1.7203106 0.1091

r = 0.431

r ² = 18.5%