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A number of investigations have focused on the problem of assessing weights that can be lifted in a safe manner. A particular article proposed using a regression model to relate the following dependent variable (y) to k = 3 independent (predictor) variables. y = individual's rating of acceptable weight (kg) x1 = extent of left lateral bending (cm) X2 = dynamic hand grip endurance (seconds) X3 = trunk extension ratio (N/kg) Suppose that the model equation is the following and that o = 6. y = 31 + 0.88x1 + 0.07x2 - 4.30x3 + e (a) What is the population regression function? (b) What are the values of the population regression coefficients? B1 = B2 = B3 = (c) Interpret the value of B 1. When ---Select--- are fixed, the mean ---Select-- | in rating of acceptable load associated with a ---Select--- | increase in ---Select--- vis 0.88 kg. (d) Interpret the value of B3. Where ---Select--- are fixed, the mean ---Select--- |in rating of acceptable load associated with a ---Select--- | increase in ---Select--- |is 4.30 kg. --Select- dynamic hand grip endurance and trunk extension ratio Need Hel extent of left lateral bending and trunk extension ratio extent of left lateral bending and dynamic hand grip enduranceA statistical program is recommended. A paper gave the following data on n = 11 female black bears. Age Weight Home-Range (years) (kg) Size (km2) 10.5 54 43.2 5.5 40 46.6 28.5 62 57.5 6.5 55 35.7 7.5 56 62.2 6.5 62 33.8 5.5 42 39.7 7.5 40 32.3 11.5 59 57.1 9.5 51 24.4 5.5 50 68.6 (a) Fit a multiple regression model to describe the relationship between y = home-range size and the predictors x, = age and x, = weight. (Round your answers to four decimal places.) y = 1 x 1 + 1 1X 2 (b) Construct a normal probability plot of the 11 standardized residuals. Standardized Standardized Standardized Standardized Residual Residual Residual Residual 70 2.0 30 2.0 1.5 20 1.5 60 . 1.0 1.0 10 50 0.5 . . 0.5 Normal Normal Normal Normal 10 0 2 Score -1 .0 2 Score -1 2 Score - 0.5 2 Score . -10 -0.5 30 -1.0 -1.0 -20 O @0 -1.5 GO -1.5 ABased on the plot, does it seem reasonable to regard the random deviation distribution as approximately normal? Explain. O The plot is reasonably straight, indicating that the assumption of normality of the random deviation distribution is not justified. O The plot is nonlinear, indicating that the assumption of normality of the random deviation distribution is not justified. The plot is reasonably straight, indicating that the assumption of normality of the random deviation distribution is justified. O The plot is nonlinear, indicating that the assumption of normality of the random deviation distribution is justified. (c) If appropriate, carry out a model utility test with a significance level of 0.05 to determine if at least one of the predictors age and weight is useful for predicting home range size. State the null and alternative hypotheses. OH,: B1 = B2 =0 H : at least one of B, or B, is not 0. O H: At least one of B, or B, is not 1. He: B1 = B2 = 1 O H : At least one of B, or B, is not 0. Ha : B1 = B2 = 0 O Ho: B1 = B2 = 1 He : at least one of B, or B, is not 1. Calculate the test statistic. (Round your answer to two decimal places.) F = What can be said about the P-value for this test? O P-value > 0.100 O 0.050 0.100 O 0.050 0.100 O 0.050