Regression - Quantitative Techniques - Assignment, Exercises of Quantitative Techniques

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Quantitative Techniques in Sociology Homework Assignment #10: Regression

Name: _________________________ Student ID#: _______________ Lab Time: _______

Complete the following questions on a separate sheet of paper. Be sure to: 1) show all of your work,

2. clearly label each problem, 3) put a box around your final answer, 4) use a pencil, 5) type definitions, 6) present your work in a neat and orderly fashion, and 7) staple this cover sheet to your other pages of completed work (do not paper-clip or fold). Remember, homework assignments are designed to help you prepare for exams. The material covered within assignments will be very similar to what appears on each test. Mastery of this material is crucial to pass this course. If you cannot complete these problems by yourself, and in a reasonable amount of time, you will not be able to pass the exam. If you are having troubles figuring out any of the material below see your lab instructor immediately. Each item is worth up to 5 points; for a possible total of 120 points.

3. Define each of the following concepts in your own words. Give a complete and specific definition and illustrate the concept by giving examples.

a) Correlation Coefficient b) Coefficient of Determination c) a & e d) ρ (rho) e) Bivariate Regression

2. As a researcher you are interested in finding out whether education is related to annual income. You collect data on a randomly selected group of adults. You record: 1) how many years of education each person has obtained and 2) their annual income (in thousands of $). The adults in your sample yielded the following data:

Annual Income (in thousands of $) Years of Education 27 13 45 17 18 9 44 19 17 6 45 24

a) Compute and interpret the regression coefficient (b).

b) Compute and interpret the intercept (a).

c) Write the regression equation using the values of b and a calculated above.

d) What annual income would you predict an average person who has 16 years of education to have?

e) What type of relationship is there between years of education and annual income?

f) Compute and interpret r and r^2.

g) Your think that years of education may be positively related to annual income. Test this relationship at the .01 significance level. Be sure present your decision in the proper form and interpret your answer.

3. Suppose you believe that the number of absences a student has in a semester decreases their final course grade. You decide to explore this relationship by taking a random sample of 10 students from a sociology course. By doing so you obtain the following data:

Final Grade Number of Absences 43 9 87 3 95 1 72 6 85 2 81 4 63 5 90 1 82 3 92 0

a) Compute and interpret the regression coefficient (b).

b) Compute and interpret the intercept (a).

c) Write the regression equation using the values of b and a calculated above.

d) Using the above equation, estimate the final grade for a person with 10 absences.

e) What type of relationship is there between final grade and number of absences?

f) Compute and interpret r and r^2.

g) As a researcher you think that the number of absences a student has may decrease their final course grade. In order to determine whether the two variables are related at the .05 significance level, and in the hypothesized direction, you test the null hypothesis. Be sure present your decision in the proper form and interpret your answer.

4. Computer Assignment* (be sure to attach a copy of your output) :

a) Choose two continuous variables. Construct a research hypothesis of the relationship between these variables. Explain why you think there is a relationship between these variables.

b) For the above example, compute and interpret the regression coefficient.

c) Compute and interpret the intercept.

d) Write the regression equation using the values of the regression coefficient and intercept calculated above. Pick one observation from your sample. Use the value of the independent variable and your regression equation to predict the value of the dependent variable for the observation that you picked. What is the error of this prediction?

e) Compute and interpret r and r^2.

• Commands will be presented in lab.