1. Testosterone is known to predict aggressive behavior and is involved in face shape during puberty. Does face shape predict aggression? Researchers measured the face width-to-height ratio of 21 university hockey players with the average number of penalty minutes awarded per game for aggressive infractions. Face ratio (x) Penalty minutes (y) 1.59 0.44 1.67 1.43 1.65 1.57 1.72 0.14 1.79 0.27 1.77 0.35 1.74 0.85 1.74 1.13 1.77 1.47 1.78 1.51 1.76 1.99 1.81 1.06 1.83 1.20 1.83 1.23 1.84 0.80 1.87 2.53 1.92 1.23 1.95 1.10 1.98 1.61 1.99 1.95 2.07 2.95 a) Calculate the means ofthe two variables ratio? b) How steeply does the number of penalty minutes increase per unit increase in face c) Calculate the estimate of the intercept? d) Write the result in the form of an equation for the line 2. Using the previous data: a) Calculate the residual mean square b) Calculate the standard error ofthe slope (b) c) How many degrees of freedom does this analysis have? d) Calculate the t-statistic e) Find the critical value fort () What is your final conclusion about the slope