2. (15 points) The table below displays data on "hours of sleep per night" (Y), "number of chil- dren" (X1), and "years of education" (X2) for a sample of 15 parents with additional informa- tion on the means, variances, and covariances for each variable. Conduct a multiple regression analysis using the preliminary calculations below. Round to four places beyond the dec- imal point during your calculations and for the final answers for each question part. Respondent Sleep Children Education 3.5 11 22 12 X1 = 3.20 12 X2 = 15.40 20 Y = 6.10 15 10 87 = 2.8857 13 5= 11.6857 - = 2.3286 Syl = -1.0929 18 $92 = 2.4929 17 $12 = -2.3000 14 18 Calculate each of the following: (a) All zero-order correlation coefficients (b) The partial correlation coefficients c) The unstandardized partial slopes (d) The y-intercept (e) The coefficient of multiple determination Interpret each of the following: (f) Discuss the zero-order and partial correlation coefficients. What is the purpose of partial correlation? What do these results say about the relationships between variables? (g) Write the regression results as an equation. Interpret each component. How would you describe these relationships? (h) Include an interpretation for the coefficient of multiple determination. What does it say about the relationship between these variables