Question

The accompanying table provides data for the sex, age, and weight of bears. For sex, let 0 represent female and let 1 represent male. Letting the response (y) varieble represent weight, use the dummy variable of sex and the variable of age and to find the multiple regression equation, Use the equation to find the predicted weight of a bear with the characteristics given below. Does sex appear to have much of an effect on the weight of a bear? a Female bear that is 24 months of age b. Male bear that is 24 months of age m Click the icon to view the bear measurement data. Find the multiple regression equation with weight as the response variable and the dummy variable of sex and the variable of age as the explanatory variables. Weight (Round to one decimal place as needed.) Sex + Age

Answer 1

calculate the regression equation for the given data by using Minitab as follows: Instructions: Import data into Minitab work sheet. Go to Stat > Regression > Regression Fit regression Model... Choose weight as response variable and sex and age as continuous predictor. Click OK. The resultant output is as shown below: Regression Analysis: Weight versus Sex, Age Analysis of Variance Source Regression DF Adj SS Adj MS F-Value P-Value 0.000 2 502225 251113 47.01 0.000 Sex 85097 85097 15.93 0.000 Age 473201 473201 88.59 51 272428 Error 5342 Lack-of-Fit 40 250953 6274 3.21 0.021 Pure Error 11 21475 1952 Total 53 774653 Model Summary R-sq R-sq(adj) R-sq(pred) 63.45% 73.0871 64.83% 55.75% Coefficients Term Coef SE Coef T-Value P-Value VIF 0.849 Constant 4.4 22.9 0.19 21.2 Sex 84.5 3.99 0.000 1.03 Age 2.841 0.302 9.41 0.000 1.03 Regression Equation 4.4 + 84.5 Sex + 2.841 Age Weight = From the above output, the regression equation is given by, Weight (ŷ) = 4.4 + 84.5sex(x, ) +2.841Age(x, ) 2) a) Calculate the predicted weight of female bear that is 24 months by using above regression equation. Weight (ŷ) = 4.4+ 84.5sex(x,)+2.841Age(x,) = 4.4 + 84.5 (0) + 2.841(24) = 72.58 = 73 The predicted weight of female bear that is 24 months is 73.

b) Calculate the predicted weight of male bear that is 24 months by using above regression equation. Weight (ŷ) = 4.4 + 84.5sex(x, ) +2.841Age(x,) = 4.4 +84.5(1) + 2.841(24) = 157.08 z 157 The predicted weight of male bear that is 24 months is 157. 3) From the given scenario, the null and alternate hypotheses can be stated as follows: Н. : В — 0 H : B, + 0 Calculate the test statistic as follows: From the coefficients table in the above output, SE B = 84.5, SE = 21.2 84.5 21.2 = 3.99 [Excel function P =T DIST.2T (t, (n-k – 1)) n- number of observations = 54 k - Number of independent terms = 2 =T.DIST.2T (3.99.(54 – 2 – 1)) = 0.000 The P-value of the test is less than the level of significance 0.05. thus, the researcher can reject the null hypothesis. There fore, one can conclude that sex variable has much effect in predicting the weight of bears.