1.Use the dataset low_birth_weight_infants.dta

link (download jpg file): https://convertio.co/download/a5231ac96a222e39b2ae2f8f9fc0ea17d83e47/

If you use statistical software, please show your work. Thanks.

A. Do a linear regression to model birth weight as the dependent variable and gestational age as the independent variable:

The equation is: _____________________

The coefficient of determination is: ______________________

The p-value for the slope is: ___________________

B. Add length as another independent variable to the above regression model.

The equation is: _____________________

The coefficient of determination is: ______________________

The p-value for the gestage coefficient is: ___________________

The p-value for the length coefficient is: ___________________

Do you think the model improves by adding length as an independent variable (yes/no) _____? Explain.

C. Compute a 95% confidence interval for the true mean of birth weight with a gestational age of 31 weeks and a length of 40 cm. Round off to whole numbers. (Please show equation and work for this.)

D. Create an interaction term by multiplying gestational age and length. Add the interaction term to the model that already includes gestage and length. Fill in the table (left column without interaction, right column with interaction term).

Independent variables

gestage, length gestage, length, gestlength

I) p-value, gestage coefficient

II) Std error, gestage coefficient

III) p-value, length coefficient

IV) Std error, length coefficient

V) Coefficient of determination

E. What principle accounts for the changes in p-value and standard error?

F. Since the coefficient of determination rose slightly, would you include the interaction term in the model? Why or why not?