Regression Project Guidelines

Data source:

SPSS survival manual 4e, 2010 by Julie Pallant. You need to refer to this under heading labeled "data source" in your report.

The author obtained the scaled scores of the following variables from an experiment in psychology through a set of survey questions answered by the respondents.

Dependent variable (DV):

tpstress: total perceived stress

Independent variable (IDV):

toptim: total optimism

tmast: total mastery

tposaff:total positive affect

tnegaff:total negative affect

tlifesat:total life satisfaction

sex: 1 if male; 2 if female

age:in years

Note: You will apply the following guidelines and class notes on the data given by your instructor.

• Split your data sample randomly as shown in the class - Calibration (80%) and Test (20%). Run descriptive tests on your regression dependent variable (DV).Identify outliers if any by "mean 3*standard deviation."Keep the outliers for regressions.
• Use analysis of descriptive statistics to summarize the data. Comment on the findings.
• Develop an estimated regression equation (regression model) and use that to predict your DV in the test sample. Identify which independent variables are statistically significant. Use variable names from the header row in the data file to write the regression equation.

Calibration Sample:

• Run correlation on all variables (except sex) on the calibration sample.Analyze.
• Run regression on the calibration sample (include sex and all other IDVs).
• Write your model equation.Report adjusted R² and other relevant statistics as discussed in the class.

Test Sample:

• Predict your DV values on test sample using the regression model equation from calibration.
• Report Generalization mean squared errors (prediction accuracy).

Analytical Report:

The report will consist of three sections in one single word file:

1. (Section 1) Summarize results on three single-spaced pages (maximum).

As discussed in the class, summary pages should contain brief descriptions of the following: Problem description or research question, data sources, DV descriptive statistics, correlation, normality assumptions, regression model equation, model estimation and fit statistics, normality plot, residual plots, model generalization, conclusion and recommendation.

1. (Section 2) Cut and paste your results and plots analyzed in section 1 from your Excel file.
2. (Section 3) Data columns for all the regression variables in the test file only, random number, forecast of DV, error and squared error. The MSE test number needs to be there. Do not keep any extra columns that you may have generated to do the project.

Note: The total number of pages of the report can be more than 3 pages depending on your section 2 and section 3.

Thresholds:

You will use the thresholds for correlation numbers (weak/moderate/strong) as discussed in the class. You will use 1 from 0 to report about your skewness and kurtosis statistics. You will use 0.7 for determination of potential multi-collinearity. For outlier detection of the DV you will use "mean 3*standard deviation" method. For correlation (could be positive or negative) you will use the rule: absolute value between 0 and 0.3 - weak correlation, between 0.3 and 0.5 moderate correlation and greater than 0.5 strong correlation.

Model Generalization:

To test the generalization power of your model, you need to split the sample into 80%/20%. You will use 80% data set to run the linear regression. After you run the regression, you will get a model equation. You will also get an estimate of mean squared error (MSE of calibration data). Use the model equation to predict your DV in the test data. Note that your test data already has the actual DV value for each test observation. Compute the test MSE from the actual DV and the predicted DV. If the two MSEs (one from the regression output and one from the test data) are close (i.e. MSE_test is not more than 1.5*MSE_calibration) your model is generalizing. Your task is to report correctly the two MSE numbers and conclude whether the model is generalizing or not. Based on your overall analysis report whether the model is implementable or not.

Rubric Template:

Rubrics Item

Type of Rubric scale

MP = maximum point

Lesson Level Learning (LLL Objectives

Scores for point rubric

0

1

2

Research Question (RQ)

3 point

MP=2

Recall hypothesis testing concepts

No RQ in the report

OK RQ

Good RQ

Data Source

3 point

MP=2

Learn not to plagiarize

No mention of data source

With mistakes

Correct

Data Splitting

Continuous

MP=10

Learn how to test before implementing a model

Descriptive Statistics

Continuous

MP=6

Recall characteristics of location/spread/skewness/kurtosis statistics

Correlation Analysis

Continuous

MP=10

Recall the learning about how two variables co-vary

Regression Analysis and Results

Continuous

MP=60

demonstrate understanding of the following topics: contrast between categorical and continuous valued independent variables (IDV), contrast between dependent variables (DV) and IDV; apply understanding of research hypotheses to interpret regression results; examine hypothesis test results and model fit

Residual Analysis and normality plot

Continuous

MP=5

Understand whether homoscedasticity assumption and normality assumption are be held true in the data

Generalization & conclusion

Continuous

MP=5

draw inferences and find evidence to support generalization

Outline for project documents:

You need to summarize the research question and analysis of regression/generalization results in section 1 (maximum 3 pages), present the results (cut of paste of tables and plots from the Excel results) in section 2, and generalization results (prediction, prediction errors, and MSE from all the test sample points) in section 3. The total number of pages of the whole report can be more than three pages based on your section 2 and 3. I give below the headings as the I had discussed in the recorded and live sessions. You can choose other suitable headings if you want.

Section 1 headings (analysis on results reported in section 2):

Research question

Data source

Descriptive statistics

Report and analyze - mean/standard deviation/skewness/kurtosis/outliers. Report whether the data violated the normality assumption.

Correlation analysis

Analyze and report two categories of correlations I discussed in the sessions

Regression results

Adjusted R², F-stat, p-value, estimates of IDV coefficients, regression equation, t-tests for identification of significant IDVs, residual analysis plots, and, normality plot

Generalization results on test sample

Analyze the results comparing MSE_calib and MSE_test.

Conclusion about Implementation

Conclude whether the model is implementable by summarizing the regression and the generalization results

sex 1 2 2 2 2 2 1 2 2 2 2 1 1 2 1 2 2 2 2 2 2 1 2 2 1 1 1 2 1 1 1 2 2 1 1 2 1 2 1 1 1 2 1 1 2 2 2 1 1 2 1 2 1 2 1 2 2 1 2 2 1 1 2 2 2 2 2 2 1 2 1 1 1 1 1 1 2 1 2 2 2 2 2 2 1 1 1 2 1 2 1 2 2 2 2 2 1 2 2 2 2 2 2 1 1 2 1 2 2 2 1 2 1 2 2 2 1 1 2 1 2 1 2 2 2 2 2 1 1 1 2 1 1 2 2 2 2 2 1 1 1 2 2 2 1 2 1 2 2 2 2 1 2 1 2 2 1 2 1 1 2 1 2 1 2 1 1 2 1 2 2 1 1 2 2 2 2 1 1 2 2 2 1 2 1 2 2 2 2 2 1 1 2 1 1 2 2 1 2 1

age 45 21 42 47 41 38 39 67 22 31 45 26 51 37 33 61 33 42 45 57 60 23 55 38 27 21 37 27 31 52 64 35 22 23 56 24 36 37 50 37 40 27 51 23 37 19 48 50 49 36 45 18 22 19 27 46 20 55 23 30 22 23 25 46 22 20 49 42 37 20 22 25 26 22 24 51 45 47 21 41 25 26 23 51 48 37 39 40 33 27 32 50 35 50 38 48 54 36 68 74 35 37 39 50 33 23 54 23 41 49 22 22 27 32 38 41 23 21 43 40 31 49 52 36 19 58 65 22 43 22 22 31 46 53 24 42 45 70 46 42 35 34 36 44 31 29 46 23 49 44 23 42 29 66 21 41 35 28 36 36 27 70 35 33 35 22 56 23 31 49 31 63 36 48 30 26 21 20 26 22 21 44 26 26 32 41 40 44 48 18 54 47 74 65 45 21 48 33 44 45

tmast 21 22 25 20 16 21 21 17 20 26 27 27 24 22 19 26 25 20 25 19 23 13 28 21 22 23 26 21 15 26 25 20 17 25 20 18 17 23 26 27 25 22 27 20 27 24 14 21 16 21 28 12 25 19 24 23 20 23 25 15 23 21 24 17 18 21 22 21 26 14 24 23 24 28 20 26 19 19 18 25 25 22 21 26 22 23 18 19 20 26 24 18 20 17 28 15 21 24 28 23 17 25 20 17 22 21 16 19 23 20 22 17 25 26 24 23 22 24 18 25 19 27 19 19 14 26 28 23 25 22 25 19 24 16 27 23 20 15 28 22 17 26 23 23 22 28 19 18 25 22 27 21 23 27 21 28 18 17 26 27 14 23 28 21 19 18 25 21 28 27 27 24 27 16 19 27 18 19 16 24 19 28 24 20 23 28 20 23 25 23 20 23 22 19 20 26 20 19 21 26

tposaff 36 37 32 30 23 40 35 35 34 40 41 39 33 38 35 40 34 19 36 37 32 20 38 31 32 33 29 43 23 41 31 33 32 37 37 32 26 19 39 29 41 36 36 22 31 42 35 20 43 31 44 11 38 22 32 35 26 39 38 32 33 40 40 40 41 28 27 37 39 24 43 21 35 40 35 36 28 30 27 40 39 37 35 32 36 41 30 28 34 25 43 39 36 39 33 31 34 27 40 43 41 45 34 26 32 39 37 37 40 37 32 30 41 21 32 41 39 33 16 35 31 42 44 30 22 32 47 34 36 44 43 27 33 26 29 23 16 32 41 40 11 37 37 34 35 45 31 28 39 31 40 33 38 42 35 35 32 26 25 35 40 29 37 26 34 36 33 30 45 28 34 30 43 31 29 46 29 26 29 31 45 38 42 22 27 40 34 40 39 33 33 34 30 37 27 22 31 26 37 31

tnegaff 15 24 16 25 24 17 35 17 36 22 17 10 12 22 15 16 15 15 22 10 25 39 14 17 33 15 20 31 29 18 14 22 31 17 22 13 22 39 24 17 15 18 12 19 15 18 27 16 25 39 14 34 14 26 21 12 30 15 18 10 14 20 10 29 12 28 28 15 12 28 19 15 22 19 18 14 20 22 16 16 15 12 23 11 10 22 32 26 14 21 14 22 28 21 12 39 11 20 10 10 23 12 26 20 13 19 33 30 26 15 15 20 33 13 20 18 21 22 39 19 20 12 13 31 36 15 13 22 12 22 13 19 13 23 17 29 23 24 10 21 20 25 26 17 18 10 19 20 12 10 15 15 17 10 19 25 19 28 17 15 23 10 19 16 25 20 16 22 15 12 14 10 16 22 30 13 35 23 31 25 29 23 20 12 17 12 16 13 15 24 20 15 12 10 17 20 21 11 12 15

tpstress 28 30 27 29 42 26 22 25 37 26 28 15 22 26 28 24 24 26 28 29 27 46 22 33 32 29 32 31 31 27 25 29 32 26 31 29 36 40 25 26 20 28 20 39 24 24 33 19 25 34 17 43 27 34 24 21 37 21 26 26 21 28 24 37 20 28 34 19 24 41 24 20 28 21 25 21 28 23 29 19 19 25 36 26 23 25 32 30 16 27 21 30 32 27 19 37 24 26 13 16 31 13 24 33 22 31 29 26 32 28 23 31 23 23 25 25 23 21 42 23 31 24 29 33 44 31 27 26 29 29 18 32 25 36 33 35 28 38 17 25 34 16 33 30 23 21 31 31 25 20 18 25 23 19 25 30 32 34 24 28 24 19 22 26 32 30 20 28 26 20 25 15 22 32 36 23 36 30 29 29 28 26 32 29 26 23 25 22 25 26 29 22 23 20 30 21 29 22 21 27

toptim 19 19 23 24 21 21 19 23 10 24 30 23 22 22 23 27 22 18 21 24 25 9 27 28 20 27 24 18 16 29 25 18 23 18 24 22 20 19 27 27 25 21 26 14 29 21 21 17 17 14 27 13 22 16 26 24 15 24 20 15 25 21 24 17 30 18 16 18 20 14 20 21 14 28 21 27 21 16 23 24 25 23 23 24 20 18 16 19 26 20 23 25 24 21 26 20 23 24 30 26 25 27 19 15 14 19 20 23 28 24 21 20 30 23 21 28 24 26 20 24 19 27 28 22 17 27 30 24 21 20 29 17 17 26 17 21 16 30 29 24 16 28 22 18 19 28 16 21 28 29 29 27 23 24 22 26 24 16 24 27 21 25 26 22 25 27 20 17 29 30 30 26 29 20 21 25 21 24 17 17 21 26 21 19 23 30 18 22 27 21 22 21 23 20 26 26 21 27 24 19

tlifesat 23 20 26 27 21 26 30 20 20 32 35 34 24 28 13 31 18 14 19 23 30 5 27 30 20 33 18 29 16 20 19 16 23 32 13 18 22 14 32 22 31 28 30 17 35 25 14 27 23 20 22 8 15 23 29 26 14 19 24 11 28 23 29 30 34 16 12 35 24 6 22 25 27 26 25 25 23 20 15 31 29 29 31 19 24 30 13 12 25 11 29 20 17 14 28 19 19 12 35 34 24 29 14 12 9 27 19 22 18 30 25 23 23 17 20 26 33 26 8 25 22 23 34 23 9 24 30 20 16 16 29 18 17 11 18 13 30 10 31 21 5 31 30 18 26 26 22 22 30 29 32 29 24 35 26 27 25 29 20 21 27 32 27 25 10 17 30 20 27 28 30 20 33 17 25 31 24 22 27 24 23 23 12 20 17 27 27 24 29 21 24 21 26 18 17 27 19 31 16 23