The following model is a simplified version of the multiple regression model used by Biddle and Hamermesh (1990) to study the tradeoff between time spent sleeping and working affecting sleep: sleep Bo + B totwrk + u where sleep and totwrk (total work) are measured in minutes per week. Answer the following questions based on the data for 15 adults from UM (Table 1). Show your manual calculation clearly. Table 1 1 23 4 5 6 or 7 8 9 PH2SHS 10 11 12 13 14 15 SLEEP TOTWRK 3438 3113 2920 2670 3083 3448 4063 3180 2928 3368 3018 1575 3295 3798 3008 3248 5020 2815 3786 2580 1205 2113 3608 2353 2851 6415 370 2438 2693 2526 (a) Draw a scatter plot. Series totwrk on the X-axis and series sleep on the Y-axis. (b) Compute the Pearson correlation coefficient. Is it significant at 5% level of significance. (c) Calculate the o and B. (d) Compute the interval estimate for the totwrk at 5% level of significance. (e) Test whether tradeoff exits between time spent sleeping and working at 1% level of significance. (f) How much is the goodness of fit? Interpret your result.