Bluman A.G. Elementary Statistics- A Step By Step Approach

Section 10–1 Scatter Plots and Correlation 541Step 2Find the values of xy, x 2 , and y 2 and place these values in the correspondingcolumns of the table.The completed table is shown.Cars x Revenue yCompany (in 10,000s) (in billions) xy x 2 y 2A 63.0 7.0 441.00 3969.00 49.00B 29.0 3.9 113.10 841.00 15.21C 20.8 2.1 43.68 432.64 4.41D 19.1 2.8 53.48 364.81 7.84E 13.4 1.4 18.76 179.56 1.96F 8.5 1.5 12.75 72.25 2.25x 153.8 y 18.7 xy 682.77 x 2 5859.26 y 2 80.67Step 3 Substitute in the formula and solve for r.nxy xyr 2[nx 2 x 2 ][ny 2 y 2 ]6682.77 153.818.72[65859.26 153.8 2 ][680.67 18.7 2 ] 0.982The correlation coefficient suggests a strong relationship between thenumber of cars a rental agency has and its annual revenue.Example 10–5Absences and Final GradesCompute the value of the correlation coefficient for the data obtained in the study ofthe number of absences and the final grade of the seven students in the statistics classgiven in Example 10–2.SolutionStep 1 Make a table.Step 2 Find the values of xy, x 2 , and y 2 ; place these values in the correspondingcolumns of the table.Number of Final gradeStudent absences x y (%) xy x 2 y 2A 6 82 492 36 6,724B 2 86 172 4 7,396C 15 43 645 225 1,849D 9 74 666 81 5,476E 12 58 696 144 3,364F 5 90 450 25 8,100G 8 78 624 64 6,084x 57 y 511 xy 3745 x 2 579 y 2 38,993Step 3 Substitute in the formula and solve for r.r nxy xy2[nx 2 x 2 ][ny 2 y 2 ]73745 575112[7579 57 2 ][738,993 511 2 ] 0.94410–9