In the following models, and are variables and and are parameters, and is an unobserved population error.

In which models can the parameters be estimated (following a suitable transformation if necessary) using ordinary least squares?

Let

where is a dummy variable which takes on value of 1 if an individual is Catholic, zero otherwise; and is a dummy variable which takes on a value of 1 if an individual lives in an urban area, zero if they live in a rural area.

What is the predicted number of kids for an individual who is Catholic and lives in an urban area?

Let

where is a dummy variable which takes on value of 1 if an individual is Catholic, zero otherwise; and is a dummy variable which takes on a value of 1 if an individual lives in an urban area, zero if they live in a rural area.

What does  measure?

Suppose that a 95% confidence interval for the regression coefficient  is given by . Is the regressor statistically significant in a two-sided test at the 5% significance level?

Suppose that we estimate a linear regression equation with 3 explanatory variables and a constant, using a sample of 65 observations, and we obtain an R-squared = 0.3177. Compute to two decimal places the sample value of the F statistic for testing the joint significance of the regressors.

The following equation reports the results of a multiple regression model estimated using OLS: The standard error of the regression is reported to be and its total sum of squares is also reported to be . Based on this information,

Suppose we use OLS to estimate the parameters of the model explained in the previous question and we denote the estimated model by: and we denote the standard error of by . The statistic has:

Using the data explained in the previous question we have estimated the following equation using OLS: where the number in parentheses below each parameter estimate is its standard error. Which one of the following statements is correct?

In the multiple regression of the previous question, the F-statistic for the overall significance of the model has an