Life insurance companies are keenly interested in predicting how long their cust
ID: 3320664 • 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) You think that it would be a better regression model if only two variables, the ages of the customer’s mother and father, were used to predict longevity.
Perform a multiple regression of y on x based upon the two variables stated in the problem above.
The least squares regression equation is:
a. y hat = 6.48 + 0.47x1 + 0.43x2
b. y = 13.52 + 0.50x1 + 3.395x2
c. y hat = 3.24 + 0.45x1 + 0.44x2 + 0.01x3
d. none of the above
ii) You think that it would be a better regression model if only two variables, the ages of the customer’s mother and father, were used to predict longevity.
Perform a multiple regression of y on x based upon the two variables stated in the problem above.
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 variable “father”, is the only variable that may be linearly related to the dependent variable, holding other independent variables constant.
c. the variable “mother” 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.
Explanation / Answer
We use Minitab to solve this question,
Regression Analysis: Longevity versus mother, father
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 2 143.47 71.735 11.98 0.020
mother 1 99.24 99.239 16.57 0.015
father 1 27.18 27.184 4.54 0.100
Error 4 23.96 5.990
Total 6 167.43
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 17.3 14.0 1.24 0.284
mother 0.3858 0.0948 4.07 0.015 1.02
father 0.388 0.182 2.13 0.100 1.02
Regression Equation
Longevity = 17.3 + 0.3858 mother + 0.388 father
a multiple regression of y on x based upon the two variables stated in the problem above.
The correct option for least squares regression equation .
None of the above.
we think that it would be a better regression model if only two variables, the ages of the customer’s mother and father, were used to predict longevity the estimated regression is,
Longevity = 17.3 + 0.3858 mother + 0.388 father
Using the appropriate hypothesis tests, which independent variables are indicated as being linearly related to the dependent variable,
a. the variables “mother” and “father” may be linearly related to the dependent variable, holding other independent variables constant.
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