Question

The quality of the crange juice produced by a cerlain manufaclurer is constantly monitored. Data collected on the swectness index of an orange juice sample and amount of water-soluble pectin for 24 production runs at a juice manufacturing plant are shown in the accompanying table. Suppose a manufacturer wanls to use simple linear regression to predict the sweetness (y) from the armount of pectin (x). Find and interpret the coelficient of deternination, r,and the cceficient of EEl Click the icon to view the data. Find and interpret the coefficient of determination, . select the correct choice below and fill in the answer box within your choice i Orange Julce Data Round to three decimal places as needed.) A The coefficient o determination ? is Г Sample va ations in the amount of water soluble pectin explain 100 r2 % o the sample variation B. The coefficent of determ nation r2 is . Sample variations in the amount of water-soluble pectin do not explain 100 r2 % of the sample vari in Run Sweetness IndexPectin (ppm) 5.1 5.6 6.1 5.9 5.8 6.2 5.8 5.6 5.5 5.9 S.4 5.5 5.7 5.5 5.3 5.2 5.5 5.6 5.9 5.2 5.9 5.9 5.7 5.8 228 400 237 249 241 Click to select and enter your answer(s) and then click Check Answer

1.

Find and interpret the coefficient of​ determination,

r squared

r2. Select the correct choice below and fill in the answer box within your choice.

2.

Find and interpret the coefficient of​ determination,

r squared

r2. Select the correct choice below and fill in the answer box within your choice.

Answer 1

From the given inform ati on, Let X be the amount of pectin and Y be the sweetness index and Σ x,y: = 47204.8 Correl ati on between X and Y is obtained by using Correlation coefficientr) Cov(X,Y) 47204.8 187.8) 6193 4098.38 (187.81651621 6193 24 -52.3094 10.4659x47.2445 24 24 24 0.10 The coefficient of determination, r-[-0.1058)0.0112. Answer: A. The coefficient of determination, r2, is 1.12%. Sample variations in the amount of water-soluble pectin explain 100(+) % of the sample variation in