Assignment 7

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School

California State University, Chico *

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Course

105

Subject

Statistics

Date

Jan 9, 2024

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pdf

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Uploaded by ProfessorUniverseTarsier7

Assignment Seven: Basic bivariate regression analysis of interval/ratio variables Part I: Use APA style and formatting for all assignments, references, and citations. Yes, have a cover page, too, as well as a running head. Try Purdue Owl for an example APA style paper: https://owl.english.purdue.edu/owl/resource/560/18/ 1. For this analysis you will use your pincp variable from the previous assignment six and schl. 2. Which is your independent and which is your dependent variable? Independent: schl Dependent: pincp 3. Follow the directions in your text for demonstration 14.4 and 14.5. Make sure to turn on your weight variable, “pwgtp.” Quick note: We have an excellent data sent from the Census. They have put this data together from five years of ACS data. They have already checked and rechecked the weights etc. Other data sets are not quite so straightforward to use. 4. 14.4 will instruct you about how to run the regression analysis. Use pincp and schl. 5. Copy and paste your output tables that look like the “ Model Summary ” and “Coefficients” tables in your text on page 262. Do not worry about the ANOVA table just yet. 6. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .321 a .103 .103 75247.074 a. Predictors: (Constant), SCHL Coefficients a Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) -45746.384 100.437 -455.473 .000 SCHL 6431.887 5.349 .321 1202.376 .000 a. Dependent Variable: PINCP 7. What is the Pearson’s r for the association between education and income? The Pearson's r for the association between education and income is 0.321.

8. What is r 2 for this association? The R squared for the association between SCHL and PINCP is 0.103 or 10.3% 9. The model equation follows this format: Y=a+bX. This is the same thing as saying dependent variable = intercept + (slope * independent variable) or pincp = intercept + (slope * schl) Type out the model with the values from your “coefficients” table. PINCP = -45746.384 + (6431.887 * SCHL) 10. Using the model equation you just wrote, calculate what someone’s expected income would be if they have 12 years of education. Show your work do not just report the answer. Do the same for someone with 16 years of education. Report the expected income values using a full sentence. 12 years of education: The expected income for someone with 12 years of education is approximately $31,440.26. SCHL = 12 PINCP = -45746.384 + (6431.887 * SCHL) PINCP = -45746.384 + (6431.887 * 12) PINCP = -45746.384 + 77186.644 PINCP = 31440.26 16 years of education: The expected income for someone with 16 years of education is approximately $57,163.81. SCHL = 16 PINCP = -45746.384 + (6431.887 * SCHL) PINCP = -45746.384 + (6431.887 * 16) PINCP = -45746.384 + 102910.192 PINCP = 57163.808 11. Now you will create a scatterplot as an alternative to presenting the data as an equation. 14.5 will help you create a scatter plot for pincp and schl. 12. Copy and paste your final scatterplot with regression line that looks like the scatterplot on page 266. Make sure to add your regression line.

13. 14. Take a long look at the scatterplot. Read the information on page 266. What might you say about the direction and strength of the relationship between income and education given the scatterplot? There is a positive relationship between income and educational. 15. Finally, what does your text say you might do if you want to analyze an ordinal or nominal variable’s impact on an interval ratio variable? Look up any concepts online or in your book you are not sure about. Give an example of each suggestion your text gives. Hint: there are two options given at the end of the chapter. Discuss them both. Linear Regression with Dummy Variables: You could use a set of dummy variables to represent the categories of a nominal variable if you wanted to include a variable with several categories in your regression model. Because of this, nominal variables can be included in regression equations that normally deal with interval or ratio variables. You can recode one of the variables to match the other's level of measurement if you have a nominal variable and want to examine its association with an ordinal, interval, or ratio variable. For instance, to match the ordinal level of church attendance, they recoded people's ages into ordinal categories in the text's example. 16. Given that you are studying actual numbers about people in California who work full-time, year- round, what are some thoughts you have about getting a bachelor’s degree ? Use full sentences and your numbers etc to answer this question. Those with bachelor's degrees might be able to choose from a broader range of employment options. The data may reveal that individuals with a bachelor's degree tend to earn significantly higher incomes compared to those without one

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