Week 7 Linear Regression Exercises

26 Jun Week 7 Linear Regression Exercises

Question
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 Statisticsbutton (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:

1. Open Polit2SetC data set.

2. Click on Analyze,then click on Regression, then Linear.

3. 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.

4. 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”.

5. 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.

6. 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 SPSS Output

Simple Linear Regression SPSS Output

Descriptive Statistics

Mean

Std. Deviation

N

Family income prior month,

$1,485.49

$950.496

378

all sources

Hours worked per week in

33.52

12.359

378

current job

Correlations

Family income

Hours worked

prior month, all

per week in

sources

current job

Pearson Correlation

Family income prior month,

1.000

.300

all sources

Hours worked per week in

.300

1.000

current job

Sig. (1-tailed)

Family income prior month,

.

.000

all sources

Hours worked per week in

.000

.

current job

N

Family income prior month,

378

378

all sources

Hours worked per week in

378

378

current job

Model Summary

Model

Adjusted R

Std. Error of the

R

R Square

Square

Estimate

1

.300a

.090

.088

$907.877

a. Predictors: (Constant), Hours worked per week in current job

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

3.068E7

1

3.068E7

37.226

.000a

Residual

3.099E8

376

824241.002

Total

3.406E8

377

a.Predictors: (Constant), Hours worked per week in current job

b.Dependent Variable: Family income prior month, all sources

Coefficientsa

Model

Unstandardized

Standardized

95.0% Confidence Interval

Coefficients

Coefficients

for B

B

Std. Error

Beta

t

Sig.

Lower Bound

Upper Bound

1

(Constant)

711.651

135.155

5.265

.000

445.896

977.405

Hours worked per week

23.083

3.783

.300

6.101

.000

15.644

30.523

in current job

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a. Dependent Variable: Family income prior month, all sources

Part II: Multiple Regression SPSS Output

This part is going to begin with an example that has been interpreted for you. Analyze the output provided and read the interpretation of the data so that you will have an understanding of what you will do for the multiple regression assignment.

Descriptive Statistics

Mean

Std. Deviation

N

CES-D Score

18.5231

11.90747

156

CESD Score, Wave 1

17.6987

11.40935

156

Number types of abuse

.83

1.203

156

Correlations

CESD Score,

Number types

CES-D Score

Wave 1

of abuse

Pearson Correlation

CES-D Score

1.000

.412

.347

CESD Score, Wave 1

.412

1.000

.187

Number types of abuse

.347

.187

1.000

Sig. (1-tailed)

CES-D Score

.

.000

.000

CESD Score, Wave 1

.000

.

.010

Number types of abuse

.000

.010

.

N

CES-D Score

156

156

156

CESD Score, Wave 1

156

156

156

Number types of abuse

156

156

156

.gif”>.gif”>.gif”>

Model Summary

Model

Change Statistics

Adjusted R

Std. Error of

R Square

R

R Square

Square

the Estimate

Change

F Change

df1

df2

Sig. F Change

1

.412a

.170

.164

10.88446

.170

31.506

1

154

.000

2

.496b

.246

.236

10.41016

.076

15.352

1

153

.000

.gif”>.gif”>.gif”>.gif”>.gif”>

a.Predictors: (Constant), CESD Score, Wave 1

b.Predictors: (Constant), CESD Score, Wave 1, Number types of abuse

ANOVAc

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

3732.507

1

3732.507

31.506

.000a

Residual

18244.613

154

118.472

Total

21977.120

155

2

Regression

5396.278

2

2698.139

24.897

.000b

Residual

16580.842

153

108.372

Total

21977.120

155

a.Predictors: (Constant), CESD Score, Wave 1

b.Predictors: (Constant), CESD Score, Wave 1, Number types of abuse

c. Dependent Variable: CES-D Score

Coefficientsa

.gif”>.gif”>.gif”>.gif”>.gif”>.gif”>.gif”>.gif”>

Model

Unstandardized

Standardized

95.0% Confidence Interval for

Coefficients

Coefficients

B

B

Std. Error

Beta

t

Sig.

Lower Bound

Upper Bound

1

(Constant)

10.911

1.612

6.768

.000

7.726

14.095

CESD Score, Wave 1

.430

.077

.412

5.613

.000

.279

.581

2

(Constant)

9.584

1.579

6.071

.000

6.465

12.702

CESD Score, Wave 1

.376

.075

.360

5.035

.000

.228

.523

Number types of

2.772

.707

.280

3.918

.000

1.374

4.170

abuse

.gif”>.gif”>.gif”>.gif”>.gif”>.gif”>.gif”>

a. Dependent Variable: CES-D Score

In the regression example, we were statistically controlling for women’s level of depression 2 years earlier and attempting to determine if recent abuse experiences affected current levels of depression, earlier depression held constant.

The correlation between CES-D scores in the two waves of data collection was moderate and positive, r = .412. You can see this value in the Model Summary panel—the value of R in the first step is the bivariate correlation (i.e., r) between the two CES-D scores. Yes, R2 was statistically significant at p < .001in both steps of the regression analysis, as shown in the ANOVA panel. Using R2 increased from .170 in the first model to .246 when the abuse variable was added. The R2 change (increase) of .076 (7.6%) was significant at p<.001, as shown in the Model Summary panel, under change Statistics. This indicates that even when prior levels of depression were held constant, recent abuse accounted for a significant amount of variation in current depression scores. The availability of longitudinal data does not “prove” that abuse experiences affected the women’s level of depression, but it does offer greater supportive evidence than cross-sectional data. If we wanted to predict current CES-D scores, using prior CES-D scores and abuse experiences as predictors, the unstandardized regression equation would be as follows: Y’= 9.584 + .376 (cesdwav1) + 2.772 (nabuse). This information comes from the panel labeled Coefficients. In terms of the independent variables there are two coefficients on the panel labeled coefficients. The first is the unstandardized coefficients (b-values) which represent the individual contribution of each predictor to the model. The b-value for number types of abuse (2.772) tells us about the relationship between CES-D score (Dependent variable) and number type of abuse (independent variable). These values are used when making predictions and they tell us to what degree the independent variable affects the outcome when the effects of all other variables in the equation are held constant. For example, the interpretation of number, types of abuse is as follows: For each unit increase in the number, types of abuse, the CES-D score (depression) increases by 2.772 units. The increase is dependent on the units that the variable is measured in. So, for each additional type of abuse reported the CES-D depression score will increase by 2.772 points. Always check the value in the significance column to determine if the variables are making a significant contribution to the model. The second coefficient reported is the standardized Beta coefficient. The standardized coefficient tells us the number of standard deviations that the dependent variable will change as a result of one standard deviation change in the independent variable. The standardized coefficient is typically used to permit the researcher to understand which of the independent variables is most important in explaining the dependent variable. In the above example, the CES-D score, Wave 1 has a Beta coefficient of .360 and the number, types of abuse has a Beta coefficient of .280. This indicates that the CES-D score, Wave 1 is the most significant predictor in the model and makes the strongest unique contribution to explaining the dependent variable. Note: When you are determining the most significant predictor ignore the negative sign if one exists. So, a predictor with a Beta of -.96 is stronger than a Beta of .55. SPSS Output for Multiple Regression Assignment Descriptive Statistics Mean Std. Deviation N CES-D Score 18.5815 11.78965 939 Respondent's age at time of 36.54749 6.234511 939 interview Educational attainment 1.57 .584 939 Currently employed? .45 .498 939 Poor health self rating .06 .247 939 Number types of abuse .85 1.160 939 Correlations Respondent' Number CES-D s age at time Educational Currently Poor health types of Score of interview attainment employed? self rating abuse Pearson CES-D Score 1.000 .061 -.155 -.220 .270 .370 Correlation Respondent's age at .061 1.000 .065 -.077 .140 -.020 time of interview Educational attainment -.155 .065 1.000 .060 -.074 -.026 Currently employed? -.220 -.077 .060 1.000 -.162 -.073 Poor health self rating .270 .140 -.074 -.162 1.000 .095 Number types of abuse .370 -.020 -.026 -.073 .095 1.000 Sig. (1-tailed) CES-D Score . .031 .000 .000 .000 .000 Respondent's age at .031 . .023 .009 .000 .272 time of interview Educational attainment .000 .023 . .032 .012 .215 Currently employed? .000 .009 .032 . .000 .012 Poor health self rating .000 .000 .012 .000 . .002 Number types of abuse .000 .272 .215 .012 .002 . N CES-D Score 939 939 939 939 939 939 Respondent's age at 939 939 939 939 939 939 time of interview Educational attainment 939 939 939 939 939 939 .gif">.gif”>.gif”>.gif”>.gif”>.gif”>.gif”>.gif”>.gif”>.gif”>.gif”>.gif”>.gif”>.gif”>

.gif”>

Currently employed?

939

939

939

939

939

939

Poor health self rating

939

939

939

939

939

939

Number types of abuse

939

939

939

939

939

939

.gif”>.gif”>.gif”>

Model Summary

Model

Change Statistics

Adjusted R

Std. Error of

R Square

Sig. F

R

R Square

Square

the Estimate

Change

F Change

df1

df2

Change

1

.348a

.121

.117

11.07693

.121

32.148

4

934

.000

2

.483b

.233

.229

10.34980

.112

136.849

1

933

.000

.gif”>.gif”>.gif”>

a. Predictors: (Constant), Poor health self rating, Educational attainment, Respondent’s age at time of interview, Currently employed?

b. Predictors: (Constant), Poor health self rating, Educational attainment, Respondent’s age at time of interview, Currently employed?, Number types of abuse

ANOVAc

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

15777.841

4

3944.460

32.148

.000a

Residual

114600.356

934

122.698

Total

130378.197

938

2

Regression

30436.854

5

6087.371

56.829

.000b

Residual

99941.343

933

107.118

Total

130378.197

938

a. Predictors: (Constant), Poor health self rating, Educational attainment, Respondent’s age at time of interview, Currently employed?

b. Predictors: (Constant), Poor health self rating, Educational attainment, Respondent’s age at time of interview, Currently employed?, Number types of abuse

c. Dependent Variable: CES-D Score

Coefficientsa

Model

Unstandardized

Standardized

95.0% Confidence Interval for

Coefficients

Coefficients

B

B

Std. Error

Beta

t

Sig.

Lower Bound

Upper Bound

1

(Constant)

22.182

2.351

9.434

.000

17.567

26.796

Respondent’s age at

.045

.059

.024

.767

.443

-.070

.161

time of interview

Educational attainment

-2.608

.624

-.129

-4.179

.000

-3.832

-1.383

Currently employed?

-4.092

.738

-.173

-5.544

.000

-5.540

-2.643

Poor health self rating

10.928

1.503

.229

7.270

.000

7.978

13.878

2

(Constant)

18.165

2.224

8.169

.000

13.801

22.528

Respondent’s age at

.068

.055

.036

1.240

.215

-.040

.176

time of interview

Educational attainment

-2.518

.583

-.125

-4.318

.000

-3.663

-1.374

Currently employed?

-3.605

.691

-.152

-5.219

.000

-4.961

-2.250

Poor health self rating

9.496

1.410

.199

6.735

.000

6.729

12.263

Number types of abuse

3.432

.293

.338

11.698

.000

2