1. Why is the standard error of an estimator often described as a measure of the precision of the estimator? A. Because the standard error of an estimator is the standard deviation of its sampling distribution and the smaller is an estimator's standard error, the narrower is its estimated confidence interval for a given significance level. B. Because the standard error of an estimator is the standard deviation of its sampling distribution and the larger is an estimator's standard error, the narrower is its estimated confidence interval for a given significance level. C. Because the standard error of an estimator is a measure of the distance between the expected value of an estimator and the population parameter. D. Because the standard error of an estimator is used to construct confidence intervals of the estimator. E. Because the standard error gives a measure of the deviation of an estimator from the true population parameter.

2. Choose the correct statement below. A. r2 is given by the ratio of the explained sum of squares and the residual sum of squares. B. r2 is a summary measure of how well the SRF approximates the PRF. C. The residual sum of squares is given by (Y^iY)2. D. Given two regression models, the one with the lower r2 value is always a more accurate model than the one with the lower r2 value. E. The coefficient of determination, r2, provides a summary measure of how well the SRF fits the data.

3.The assumption of normally distributed errors means that... A. the regression model will not be subject to specification error. B. errors can be ignored when doing regression modelling. C. the OLS estimators can also be assumed to be normally distributed since they are minimum variance. D. the OLS estimators can also be assumed to be normally distributed since they are BLUE. E. the OLS estimators can also be assumed to be normally distributed since they are a linear functions of the errors.

4. The assumption of normally distributed errors means that... A. the regression model will not be subject to specification error. B. errors can be ignored when doing regression modelling. C. the OLS estimators can also be assumed to be normally distributed since they are minimum variance. D. the OLS estimators can also be assumed to be normally distributed since they are BLUE. E. the OLS estimators can also be assumed to be normally distributed since they are a linear functions of the errors.

5. A feature that interval estimates (such as confidence limits) have, and which point estimates do not, is that... A. it increases confidence in the regression model. B. it reduces uncertainty of the regression model. C. it incorporates uncertainty that arises due to sampling. D. it gives a range of values which have some defined probability of containing the parameter value. E. it provides a range of equally likely values instead of a single highly unlikely value.

6. Estimating the confidence interval for the variance of regression requires the statistic: 2=(n2)^22 which follows... A. the standard-normal distribution. B. student's t distribution. C. the normal distribution. D. the F distribution. E. the chi-square distribution.

Part 2 7. Consider the following data on the body-mass-index value (BMI) and monthly income (INC), measured in thousands of rands, for a sample of 10 working adults. \\ AdultBMIINCA3312B2523C298D236E2218F2425G2213H309I2818J3022 Use these data to estimate the constant and slope coefficient of the SRF: BMI=f(INC).

How would you interpret this estimated slope coefficient? A. An one thousand rand higher monthly salary is, on average, associated with a relatively large decrease in the BMI measure. B. An one thousand rand higher monthly salary is, on average, associated with a slightly higher BMI measure. C. People with higher incomes likely consume healthier foods than people with lower incomes. D. An one thousand rand higher monthly salary is, on average, associated with a slightly lower BMI measure. E. People with lower incomes eat more than people with higher incomes.

8. What is the value of ESS (explained sum of squares) for this model?

9. What is the value for RSS (residual sum of squares) for this model?

10. What is the value of TSS (total sum of squares) for this model?

11. Given your results above, the r2 for the estimated model is given by...

12. Choose the best interpretation of the r2 value estimated for this model. A. The two variables are independent because the variation in BMI that is explained by variation in income is close to zero. B. It is a good model for explaining variation in BMI. C. A small proportion of the variation in BMI is explained by variation in monthly income. D. A large proportion of the variation in BMI is explained by variation in monthly income. E. There is a weak correlation between BMI and monthly income.

13. Based on your regression results above, on average, a R1000 increase in income is associated with a change in BMI of...

14.What is the value of the estimated intercept term?