Question

The data set 401KSUBS.RAW contains information on net financial wealth (nettfa), age of the survey respondent (age), annual family income (inc), family size (fsize), and participation in certain pension plans for people in the United States. The wealth and income variables are both recorded in thousands of dollars. For this question, use only the data for single-person households (so fsize = 1).

(i) How many single-person households are there in the data set?

(ii) Use OLS to estimate the model

and report the results using the usual format. Be sure to use only the single-person households in the sample. Interpret the slope coefficients. Are there any surprises in the slope estimates?

(iii) Does the intercept from the regression in part (ii) have an interesting meaning? Explain.

(iv) Find the p-value for the test H0: ft2 = 1 against H0: ft2<1. Do you reject H0 at the 1% significance level?

(v) If you do a simple regression of nettfa on inc, is the estimated coefficient on inc much different from the estimate in part (ii)? Why or why not?

Answer 1

(i)

In the referred data, the variable f size is used for family size. Single person family is denoted by 1. Import the data in MS-Excel and use filter to obtain the number of single person family. Therefore, there aresingle people in the sample of 9,275.

(ii)

The data is shown below:

The estimated model is written below:

The required estimated model can be obtained in Minitab by using below steps:

1. Go to Stat > Regression > Regression as shown in the below screenshot:

2. The below dialog box opens. Enter the required variables corresponding to “Response” and “Predictors” headings. The updated dialog box is shown below:

3. Click OK to get the below output:

The estimated equation is:

And:

The coefficient on inc represents that extra single dollar in income is imitated in about 80 more cents in estimated nettfa. The coefficient on age means that, if an individual becomes older by one year, his/her nettfa is estimated to increase by about $843. Both interpretations are not surprising.

(iii)

The intercept obtained above does not seems to be interesting because it provides the estimated nettfa for inc = 0 and age = 0. It can conclude that there is none of them even close to these values in the appropriate population.

(iv)

From the output obtained in part (ii), it can conclude that the p-value for ageis 0.000 that is less than the considered level of significance 0.01. Therefore, the null hypothesis may be rejected at 1% level of significance.

(v)

The estimated model is written below:

The required estimated model can be obtained by using below steps:

1. Go to Stat > Regression > Regression as shown in the below screenshot:

2. The below dialog box opens. Enter the required variables corresponding to “Response” and “Predictors” headings. The updated dialog box is shown below:

3. Click OK to get the below output:

The coefficient on inc in the simple regression output obtained above is.821 that is not very dissimilar from the .799 obtained in part (ii).