Time Submit 3. [22 pt.] A person's muscle mass is expected to decrease with age. To explore this relationship, a nutritionist built a simple linear regression model: Y = Bo + BIX +E where X is age and Y is a measure of muscle mass, and the data were collected from randomly selected 11 people as follows. Observation 1 2 Age (X) 42 43 3 49 4 Muscle mass (Y) 106 50 60 67 69 10 107 90 55 120 98 97 74 69 Sample Mean Sample Std Correlation coefficient Age (X) X = 57.82 Sx = 11.12 T = -0.906 Muscle mass (Y) Y = 90.55 Sy = 17.04 Upper critical values, where P (t > ta,af) = Q and P (F > Faaf1,dj2) - Q to.05,9-1.8331 to.025,9-2.2622 to.05,10-1.8125 to.025,10-2.2281 Fo.05,1,9 - 5.1174 Fo.025,1,9 = 7.2093 3.1) [5 pt.] Based on the sample statistics, determine the regression coefficients, bo and by . 3.2) [5 pt.] Using the coefficients estimated in Question 3.1, predict the expected muscle mass of a person whose age is 52. 3.3) [6 pt.] Is there evidence of a linear relationship between Age and Muscle mass at the 0.05 level of significance? Use t-Test for a correlation coefficient. Answer based on the critical value approach. Show the work: a) your hypotheses, b) test statistic, c) critical value, and d) decision. 02:51:13 Time Remaining Submit Upper critical values, where P (t > ta,dj ) = Q and P (F > Fadf1,d/2) = a to.05,9-1.8331 to.025,9-2.2622 to.05,10-1.8125 to.025,10-2.2281 Fo.05,1,9 - 5.1174 Fams,19 - 72093 3.1) [5 pt.] Based on the sample statistics, determine the regression coefficients, by and by . 3.2) [5 pt.] Using the coefficients estimated in Question 3.1, predict the exper ass of a person whose age is 52. 3 3.3) [6 pt.] Is there evidence of a linear relationship between Age and Muscle mass at the 0.05 level of significance? Use t-Test for a correlation coefficient. Answer based on the critical value approach. Show the work: a) your hypotheses, b) test statistic, c) critical value, and d) decision. 3.4) [6 pt.] James conducted the regression analysis with Excel, but he realized several statistics are missing in the summary table. Given the regression summary, is there evidence of arlinear effect of Age(X) on Muscle mass(Y)? Answer based on the F test in ANOVA analysis (use the critical value approach) at the 0.05 level of significance. Show the work: a) your hypotheses, b) test statistic, c) critical value, and d) decision. ANOVA df SS MS Regression 1 2382.86 Residual 521.87 Total 10 2904.73 * Paragraph . - BI U A- ATE= = X X 12pt