Use the dataset low_birth_weight_infants.dta.

(link: https://convertio.co/download/a5231ac96a222e39b2ae2f8f9fc0ea1751c11f/)

Are my answers correct? Please use statistical software to provide step-by-step explanation. Please do not copy and paste from other sources. Thanks.

Question 1: Do a linear regression to model birth weight as the dependent variable and gestational age as the independent variable:

The equation is: birthweight = -932.4038 + 70.3099 *gestation age

The coefficient of determination is: 0.4355

The p-value for the slope is: 8.15 x 10^-14 (8.15E-14) or p < .05

Question 2: Add length as another independent variable to the above regression model.

The equation is: -1441.906 + 21.394*gestation age + 51.404*length

The coefficient of determination is: 0.6871

The p-value for the gestage coefficient is: 0.0106

The p-value for the length coefficient is: 4.49 x 10^-14 (4.49E-14) or p < .05

Question 3: Do you think the model improves by adding length as an independent variable (yes/no)? yes Explain.

Yes, the regression model is improved after adding another independent variable length since the coefficient of determination has increased along with adjusted R square value and the standard error of the model has decreased. Both factors make the model better.

Question 4: 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 use statistical software to generate the results and use the equation in order to show step-by-step results. Thanks.

y= -1441.906 + 21.394*gestation age + 51.404*length

y= -1441.907 + 21.394 * 31 + 51.404 * 40

standard error: 152.5854

CI equation: (1307.46 +/- 1.96*(152.5854))

95% confidence interval: (1008.39, 1606.53)

Question 5: 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)

p-value, gestage coefficient p-value = 0.011 p-value = 0.111

Std error, gestage coefficient 8.20 60.75

p-value, length coefficient p-value = 4.40 x 10^-14 p-value = 0.4196

Std error, length coefficient 5.82 44.57

Coefficient of determination 0.6871 0.6993

Question 6: What principle accounts for the changes in p-value and standard error?

We have added a non-significant interactions in the model and due to that there is a change in the p-value and standard errors. Many independent variables can express variability in dependent variable better than just one independent variable if collinearity does not exist between independent variables.

Question 7: Since the coefficient of determination rose slightly, would you include the interaction term in the model? Why or why not?

No, we would not choose to include interaction term in the model because the other two coefficients become insignificant after adding this interaction term. The interaction is not significant in this model, so we can conclude that we will not include the interaction term in the model. I would choose not to include the interaction term because the rise in value of R-square is not high and the standard error is reduced slightly by the addition of new variable interaction.