Share
Explore BrainMass

Regression Analysis for life insurance data

Would like step-by-step guidance with the attached statistics problems.

1. Compute the regression equation (Solving of both "a" and "b") and compute the standard error of the estimate.

Sample size = 20
X= amount of disposable Income (000$)
Y= amount of life insurance (000$)
Sum of X = 334
Sum of Y = 799
Sum of X*Y=14,168
Sum of X2 = 6118
Sum of Y2=33,511

Explain the values of "a" and "b" in reference to this problem.

2. The following sample data pertain to shipments received by the U.S. Department of the Army from three different vendors.

FDX UPS CF
Rejected 12 08 20
Not Perfect But Acceptable 23 12 30
Perfect 85 60 110

Use a ten percent significance level to test whether the three vendors ship products of equal quality.

3. In Cy 2006, the American Statistical Association randomly selected ten working women ages 35 to 45; to determine the relationship between annual income (y) and years of formal education (x). The following represents their statistical findings.

Y=$1400 + $800x

a. predict the annual income for a working woman who has completed three years of formal education.

b. Would it be fair to say that each year of formal education is worth $2200? Why or why not?

4. There are 2500,000 eligible voters in Alaska of whom 37,500 are Hispanic. A random sample of 500 voters is to be selected. Determine the mean, variance, and the standard deviation of Hispanic voters.

5. Suppose that the percentage distribution of U.S. college students classed as Freshmen, Sophomores, Juniors, Seniors, Graduates and Post Graduate has been established by the 2000 census as follows:

Class Percentage Distribution
Freshmen 15
Sophomore 10
Juniors 25
Seniors 30
Graduate 15
Post graduate 05
Total 100

Suppose we took a random sample of 1000 students from a university and found the following distribution to be:

Class Percentage Distribution
Freshmen 180
Sophomore 260
Juniors 210
Seniors 150
Graduate 100
Post graduate 100
Total 1000

On the basis of the sample evidence, could we conclude that the university fits into the distribution of the CY 2000 census data or has the University applied special emphasis in some category of students? Utilize the Chi-Square distribution, testing the null hypothesis within ten percent significance level. Use a problem specific hypothesis.

Attachments

Solution Preview

Please see the attachments.
Calculations are done in excel.

1. Compute the regression equation (Solving of both "a" and "b") and compute the standard error of the estimate.

Sample size = 20
X= amount of disposable Income (000$)
Y= amount of life insurance (000$)
Sum of X = 334
Sum of Y = 799
Sum of X*Y=14,168
Sum of X2 = 6118
Sum of Y2=33,511

Explain the values of "a" and "b" in reference to this problem.

Answer

The general form of simple linear regression is Y= a + bX. Where Y is the dependent variable and X is the independent variable. a and be are known as the regression coefficients .They are estimated by the method of least squares. The estimates of a and b are given by

The parameter b measures the impact of unit change in X on the dependent variable Y. It is the slope of the regression line. The parameter a is the value of Y when X=0. It is known as the Intercept term

The regression equation can be used to predict the value of Y for a given X. The predicted value of Y is given by

The square of correlation between X and Y is known as the coefficient of determination (R2) . R2 gives the percentage of variation that can be predicated using the regression equation.

The calculated value of slope from the above equation b =1.5266 and intercept a =14.45483

The regression coefficients can be interpreted as
For a unit increase in amount of disposable Income, the amount of life insurance increase by 1.5266 units

When the value of amount of disposable Income is zero, the value of amount of life insurance = 14.45483

The standard error of estimate is given by

Where Sxx, Syy, Sxy denotes the sum of squares and cross products

Thus standard error of estimate =4.244157

2. The following sample data pertain to shipments received by the U.S. Department of the Army from three different ...

Solution Summary

Step by step method for regression analysis is discussed here. Regression coefficients, coefficient of determination, scatter diagram and significance of regression model are explained in the solution. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

$2.19