# Linear Regression Exercises Simple Regression Research

**Week 7 Linear Regression Exercises**

**Simple Regression**

Research Question: Does the number of hours worked per week (*workweek*) predict family income (*income*)?

Using Polit2SetA data set, run a simple regression using Family Income (*income*) as the outcome variable (Y) and Number of Hours Worked per Week (*workweek*) as the independent variable (X). When conducting any regression analysis, the dependent (outcome) variables is always (Y) and is placed on the y-axis, and the independent (predictor) variable is always (X) and is placed on the x-axis.

Follow these steps when using SPSS:

- Open Polit2SetA data set.
- Click on
**Analyze**, then click on**Regression**, then**Linear**. - Move the dependent variable (
*income*) in the box labeled “Dependent” by clicking the arrow button. The dependent variable is a continuous variable. - Move the independent variable (
*workweek*) into the box labeled “Independent.” - Click on the
**Statistics**button (right side of box) and click on**Descriptives**,**Estimates**,**Confidence Interval**(should be 95%), and**Model Fit**, then click on**Continue**. - Click on
**OK**.

__ Assignment:__ Through analysis of the SPSS output, answer the following questions.

- What is the total sample size?
- What is the mean income and mean number of hours worked?
- What is the correlation coefficient between the outcome and predictor variables? Is it significant? How would you describe the strength and direction of the relationship?
- What it the value of R squared (coefficient of determination)? Interpret the value.
- Interpret the standard error of the estimate? What information does this value provide to the researcher?
- The model fit is determined by the ANOVA table results (
*F*statistic = 37.226, 1,376 degrees of freedom, and the*p*value is .001). Based on these results, does the model fit the data? Briefly explain. (Hint: A significant finding indicates good model fit.) - Based on the coefficients, what is the value of the y-intercept (point at which the line of best fit crosses the y-axis)?
- Based on the output, write out the regression equation for predicting family income.
- Using the regression equation, what is the predicted monthly family income for women working 35 hours per week?
- Using the regression equation, what is the predicted monthly family income for women working 20 hours per week?

**Multiple Regression**

__ Assignment:__ In this assignment we are trying to predict CES-D score (depression) in women. The research question is: How well do age, educational attainment, employment, abuse, and poor health predict depression?

Using Polit2SetC data set, run a multiple regression using CES-D Score (*cesd*) as the outcome variable (Y) and respondent’s age (*age*), educational attainment (*educatn*), currently employed (*worknow*), number, types of abuse (*nabuse*), and poor health (*poorhlth*) as the independent variables (X). When conducting any regression analysis, the dependent (outcome) variables is always (Y) and is placed on the y-axis, and the independent (predictor) variable is always (X) and is placed on the x-axis.

Follow these steps when using SPSS:

- Open Polit2SetC data set.
- Click on
**Analyze,**then click on**Regression**, then**Linear**. - Move the dependent variable, CES-D Score (
*cesd*) into the box labeled “Dependent” by clicking on the arrow button. The dependent variable is a continuous variable. - Move the independent variables (
*age*,*educatn*,*worknow*, and*poorhlth*) into the box labeled “Independent.” This is the first block of variables to be entered into the analysis (block 1 of 1). Click on the bottom (top right of independent box), marked “Next”; this will give you another box to enter the next block of indepdent variables (block 2 of 2). Here you are to enter (*nabuse*).**Note:**Be sure the Method box states “Enter”. - Click on the
**Statistics**button (right side of box) and click on**Descriptives**,**Estimates**,**Confidence Interval**(should be 95%),**R square change**, and**Model Fit**, and then click on**Continue**. - Click on
**OK**.

__ Assignment:__ (When answering all questions, use the data on the coefficients panel from Model 2).

- Analyze the data from the SPSS output and write a paragraph summarizing the findings. (Use the example in the SPSS output file as a guide for your write-up.)
- Which of the predictors were significant predictors in the model?
- Which of the predictors was the most relevant predictor in the model?
- Interpret the unstandardized coefficents for educational attainment and poor health.
- If you wanted to predict a woman’s current CES-D score based on the analysis, what would the unstandardized regression equation be? Include unstandardized coefficients in the equation.
**Week 7 Linear Regression Exercises****Simple Regression**Research Question: Does the number of hours worked per week (

*workweek*) predict family income (*income*)?Using Polit2SetA data set, run a simple regression using Family Income (

*income*) as the outcome variable (Y) and Number of Hours Worked per Week (*workweek*) as the independent variable (X). When conducting any regression analysis, the dependent (outcome) variables is always (Y) and is placed on the y-axis, and the independent (predictor) variable is always (X) and is placed on the x-axis.Follow these steps when using SPSS:

- Open Polit2SetA data set.
- Click on
**Analyze**, then click on**Regression**, then**Linear**. - Move the dependent variable (
*income*) in the box labeled “Dependent” by clicking the arrow button. The dependent variable is a continuous variable. - Move the independent variable (
*workweek*) into the box labeled “Independent.” - Click on the
**Statistics**button (right side of box) and click on**Descriptives**,**Estimates**,**Confidence Interval**(should be 95%), and**Model Fit**, then click on**Continue**. - Click on
**OK**.

Through analysis of the SPSS output, answer the following questions.**Assignment:**- What is the total sample size?
- What is the mean income and mean number of hours worked?
- What is the correlation coefficient between the outcome and predictor variables? Is it significant? How would you describe the strength and direction of the relationship?
- What it the value of R squared (coefficient of determination)? Interpret the value.
- Interpret the standard error of the estimate? What information does this value provide to the researcher?
- The model fit is determined by the ANOVA table results (
*F*statistic = 37.226, 1,376 degrees of freedom, and the*p*value is .001). Based on these results, does the model fit the data? Briefly explain. (Hint: A significant finding indicates good model fit.) - Based on the coefficients, what is the value of the y-intercept (point at which the line of best fit crosses the y-axis)?
- Based on the output, write out the regression equation for predicting family income.
- Using the regression equation, what is the predicted monthly family income for women working 35 hours per week?
- Using the regression equation, what is the predicted monthly family income for women working 20 hours per week?

**Multiple Regression**In this assignment we are trying to predict CES-D score (depression) in women. The research question is: How well do age, educational attainment, employment, abuse, and poor health predict depression?**Assignment:**Using Polit2SetC data set, run a multiple regression using CES-D Score (

*cesd*) as the outcome variable (Y) and respondent’s age (*age*), educational attainment (*educatn*), currently employed (*worknow*), number, types of abuse (*nabuse*), and poor health (*poorhlth*) as the independent variables (X). When conducting any regression analysis, the dependent (outcome) variables is always (Y) and is placed on the y-axis, and the independent (predictor) variable is always (X) and is placed on the x-axis.Follow these steps when using SPSS:

- Open Polit2SetC data set.
- Click on
**Analyze,**then click on**Regression**, then**Linear**. - Move the dependent variable, CES-D Score (
*cesd*) into the box labeled “Dependent” by clicking on the arrow button. The dependent variable is a continuous variable. - Move the independent variables (
*age*,*educatn*,*worknow*, and*poorhlth*) into the box labeled “Independent.” This is the first block of variables to be entered into the analysis (block 1 of 1). Click on the bottom (top right of independent box), marked “Next”; this will give you another box to enter the next block of indepdent variables (block 2 of 2). Here you are to enter (*nabuse*).**Note:**Be sure the Method box states “Enter”. - Click on the
**Statistics**button (right side of box) and click on**Descriptives**,**Estimates**,**Confidence Interval**(should be 95%),**R square change**, and**Model Fit**, and then click on**Continue**. - Click on
**OK**.

(When answering all questions, use the data on the coefficients panel from Model 2).**Assignment:**- Analyze the data from the SPSS output and write a paragraph summarizing the findings. (Use the example in the SPSS output file as a guide for your write-up.)
- Which of the predictors were significant predictors in the model?
- Which of the predictors was the most relevant predictor in the model?
- Interpret the unstandardized coefficents for educational attainment and poor health.
- If you wanted to predict a woman’s current CES-D score based on the analysis, what would the unstandardized regression equation be? Include unstandardized coefficients in the equation.