Life insurance companies are keenly interested in predicting how long their cust
ID: 3320658 • Letter: L
Question
Life insurance companies are keenly interested in predicting how long their customers will live because their premiums and profitability depend on such numbers. An actuary for one insurance company gathered data from 100 recently deceased male customers. He recorded the age at death of customer plus the ages at death of his mother and father, the mean ages at death of his grandmother and mean age of death of grandfather.
Longevity mother father gmother gfather
80 85 78 72 71
73 88 63 76 66
70 66 75 67 57
72 72 67 68 55
79 88 73 64 73
83 90 72 74 62
70 67 65 70 59
i)Determine the multiple regression of y on x for this problem; you will be predicting longevity based upon all of the variables, except for being a smoker. (do not include smoker in your regression).
Next, using the appropriate hypothesis tests, which independent variables are indicated as being linearly related to the dependent variable, as shown by results utilizing the appropriate two-tailed hypothesis tests?
a. the variables “mother” and “father” may be linearly related to the dependent variable, holding other independent variables constant.
b. the variables “mother”, “father”, “grandmother” may all be linearly related to the dependent variable, holding other independent variables constant.
c. the variable “father” is the only variable that may be linearly related to the dependent variable, holding other independent variables constant.
d. none of the independent variables are linearly related to the dependent variable.
ii) Determine the multiple regression of y on x for this problem; you will be predicting longevity based upon all of the variables, except for being a smoker. (do not include smoker in your regression).Test the validity of the regression model as demonstrated in your textbook and in class discussions. Your results indicate:
a. Since the appropriate p-value is approx 0, reject the null; the model is valid.
b. Since the standard error is between 2 and 3, reject the null; the model is valid.
c. Since the appropriate p-value is approx 0.802, do not reject the null; the model is not valid.
d. none of the above
Explanation / Answer
i)
Decision rule : if p value < 0.05, then two variables are linearly correlated
By observing p values of all the variables, the correct option is
d. none of the independent variables are linearly related to the dependent variable.
since all the p values > 0.05, none of them is significantly related with dependent variable individually.
ii) here p value = 0.21, do not reject the null
d. none of the above
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