Problem Set: Correlation and Regression

1. Use the scatterplot to discuss the overall pattern of association and any unusual points.

2. Compare the values of the correlation coefficients and the slopes with and without the bmi values greater than 35 used to estimate the model.

3. Write out the equation for the fitted regression line. State the values of the slope and intercept, including their units.

4. Interpreting the slope, part 1:

Using the standard error for the slope given by Stata, and the critical value from the t distribution, demonstrate the calculation of the confidence interval for the slope.

Explain why the degrees of freedom are 248 and why we use .025 in the upper tail of the t distribution.

Write a sentence summarizing the confidence interval for the slope, including the units.

5. Interpreting the slope, part 2:

Explain all the details in the t test for the slope with a two-sided alternative hypothesis:

State the null and alternative hypotheses:

Using the slope estimate and the standard error estimate from the output, show the calculation of the test statistic:

Carefully interpret the P value that Stata gives for this test:

State your conclusion about the population slope:

Stata list command Results for the standard errors for using y ^ to estimate the mean percent body fat for the values of bmi around 30 and around 25:

6. Explain why the standard errors for the estimated mean siri values for bmi values around 30 are larger than those the estimated mean siri values for bmi values around 25. 

(Use the formula for the standard error and the summary command you did at the beginning of this problem set.)

7. For observation number 79, who represents a population with a bmi of 25.08, use the fitted value and the standard error to calculate a 95 % confidence interval for the mean percent body fat of the population of individuals with bmi equal to 25.08. 

(You already have the t* value from your work with the slope.)                                

Stata list command Results for the standard errors for using y ^ to predict the percent body fat for individuals with values of bmi around 30 and around 25:

8. Explain why, based on the values of siri_se_ind, bmi cannot be used to precisely predict an individual's percent body fat. 

9. Interpret the value of R 2 from this regression and verify that it is the square of the Pearson correlation coefficient.

10. Interpret the standard error of the regression, the value Stata calls the root MSE, including the units.  Explain why it also tells us that using BMI to predict an individual's percent body fat will not lead to predictions that are useful in practice. (Statistics-based answer; not clinical one.)

Attachment:- Assignment Files.rar