Problem 1

To do this assignment, open the dataset included with the assignment on OWL (savings .xls).  The dataset contains information on individual’s savings deci- sions. It records their income, age, education level, and family size. Information about the dataset can be found in the file SAVING description.txt.

1. Make a scatter-plot of income (x-axis) against savings (y-axis). Does the variance of savings seem to increase with income? Provide a rationale to explain your findings.

2. Estimate βˆ0  and βˆ1  from the following simple regression model.  Report results in a concise table.

savi  = β0 + β1 inci + ui                                                     (1)

(a) Is βˆ1 statistically significant at the 95% confidence level? What about

the 99% and 90% confidence level?

(b) Save the residuals from the regression and make a scatter-plot of income (x-axis) against the residuals (y-axis).  Does the variance of the residuals seem to increase with income? Does this violate one of the statistical assumptions? If so, which one?

3. Estimate βˆ0(o) , βˆ1(o) , βˆ2(o)  from the following multiple linear regression model. Report results in a concise table.

savi  = β0(o) + β1(o)inci + β2(o)educi + ϵi                                         (2)

(a) What is the interpretation of βˆ2(o)? Be precise

(b) Are βˆ1(o)  and βˆ2(o)  statistically significant at the 95% confidence level?

(c) Is βˆ1(o)  from the second regression larger or smaller than βˆ1  from the first regression? Explain your findings.