5.1 Given the following data: 1 7 KIT834 Y 33247 Z 15 7 5 14 10 (a) Write a SAS program and compute the Pearson correlation coefficient between X and Y; X and Z. What is the significance of each? (b) Change the correlation request to produce a correlation matrix; that is, the correla- tion coefficient between each variable versus every other variable. 5.5 From the data for X and Y in Problem 5.1: (a) Compute a regression line (Y on X). Y is the dependent variable, X the independent variable. (b) What is slope and intercept? (c) Are they significantly different from zero? agression equation for pre-

Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4

1:31 A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 8 children from her practice, measures their height and head circumference, and obtains the data shown in the table. Complete parts (a) through (e) below. Click here to see the Table of Critical Values for Correlation Coefficient. Data table Critical Values for Correlation Coefficient Print ||| = n 3 0.997 4 0.950 5 0.878 6 0.811 7 0.754 8 0.707 9 0.666 10 0.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 28 0.374 29 0.367 30 0.361 n Done O Height (in.) Head Circumference (in.) 27.75 25 26.25 25.5 27.25 26.75 26 27.25 Vo) 1 LTE 4G 15% I X 17.4 17.1 17.3 16.9 17.4 17.3 17.1 17.4

(b) For each pair of variables, generate the correlation coefficient r. Compute the corresponding coefficient of determination r2. (Use 3 decimal places.)   r r2 x1, x2     x1, x3     x1, x4     x2, x3     x2, x4     x3, x4     What percent of the variation in box office receipts can be attributed to the corresponding variation in production costs? (Use 1 decimal place.)