Multiple Linear Regression and Correlation
PSYSTA2 Worksheet #1b Simple and Multiple Linear Regression and Correlati on GENERAL DIRECTIONS: Use STATISTICA as a tool to support your answers. On whole sheet s of yellow pad paper, write all your answers to this worksheet showing complete solutions in blue or black ink on ly, as demonstrated in the lectures. Support your answers by copying necessary outputs of STATISTICA into a blank MS Word document, and print the MS Word document. Stap le the computer output to your yellow pad paper.
IMPORTANT : We practice Clean-As-You-Go in all DLSU computer laboratories. This means that you can NOT save your work in the DLSU compute rs for public use. You must save any work that you do for PSYSTA2 into your own USB remo vable drive. Before leaving the laboratory, make sure that you delete all the PSYST A2 work files you have in the public computer, BY CLEARING THE DOWNLOAD FOLDER and EMPTY the Recycle Bin. ANY STUDENT WHO DOES NOT COMPLY WILL AUTOMATICALLY BE PENALIZED 10 POINTS FOR THIS WORKSHEET.
Part I: Identification (to be written on your whole sheet o f yellow pad paper) To understand how to potentially improve employee a ttitude, a large financial organization surveyed a sample of its clerical employees from it s different departments (Chatterjee and Price, 1991). Responses to the individual items from each questionnaire were then summarized into composite scores to provide measurements of attitude (overall attitude towards work), complaints (employer’s ability to handle employee complaints), privileges (work privileges/benefits), learning (how much an employee learns from the job), raises (incentives/bonuses), critical (how much critical thinking is required), and advance (career advancement/promotion opportunities).
All the seven composite scores are scaled from 1 - 100, wherein a higher score suggests more favorable rating towards the particular dimension ( e.g., attitude , complaints , etc.). Given below are the relevant STATISTICA outputs for estimating and evaluating the required regression model. 1.) Write down the fitted multiple linear regression mo del which can be used to predict attitude based on all the other 6 dimensions. 2.) Determine and interpret the coefficient of determination of this model.
3.) Perform an 8-step procedure of model adequacy using a 0.10 level of significance and an F- test with both critical value approach and p-value approach.
4.) Interpret the estimated slope coefficients of ONLY those predictors which are SIGNIFICANT at = 10% in the fitted model. 5.) Using the estimated regression model, predict the attitude score of a clerical employee in this organization who has the following (scores) profile . Show complete solutions.
Complaint Privileges Learning Raises Critical Advan ce 54 55 41 72 55 37 Part II: Hands-On Exercises A. We will use a study carried out by Roney, Mahler an d Maestripieri (2003) 1. Roney et al were examining the way that a male participant beha ved towards a confederate whom the participant believed was really another participant . They measured a number of different variables. Two of them are:
· the participant rated how desirable the confederate would be as a romantic partner; · the confederate rated how much the participant enga ged in ‘display’ behavior, for example trying to impress, showing off, talking abo ut himself.
The results are shown in the following table:
1Roney, J. R., Mahler, S. V. & Maestripieri, D. (200 3). Behavioral and hormonal responses of men to bri ef interactions with women. Evolution and Human Behavi or, 24(6), 365–375.
1.) Construct a scatterplot for this data using STATIST ICA and generate a printout.
2.) On your yellow pad paper, identify the independent and dependent variables in this study. 3.) On your yellow pad paper, find ?
?, ?, ?, ?, ?, = = = = = = ∑ ∑ ∑ ∑ ∑ n Y X Y X Y X n i n i i n i n i n i 12 1 2 1 1 1 Find the values of yy xy xxS S S , , 4.) On your yellow pad paper, compute and interpret the estimated Pearson’s r correlation coefficient between the two variables. 5.) On your yellow pad paper, find the fitted simple li near regression equation which can be used to predict the rating of display behavior using desirability of confederate as a predictor.
Interpret the estimated slope coefficient. 6.) On your yellow pad paper, assess the statistical si gnificance of the model at = 10%. In other words, perform a t-test of r to see if there exists a significant linear relati onship between the two variables. Use the 8-step critical value approa ch.
7.) On your yellow pad paper, use the fitted model to p redict the expected rating of display behavior for a desirability of confederate score of 7 and calculate the residual. Is it an overestimation or underestimation? Explain. 8.) Generate the STATISTICA output for the regression a nalysis for this problem. It should contain the answers to parts (4) to (7).
B. The US National Academy of Sciences, in one instanc e, had become interested in assessing how the ratings of research PhD programs (QUALITY ) in the country are correlated with their degree-granting departments’ academic profile (1982). The quality-ratings are presented in a standardize scale of 0 - 80, with hi gher scores meaning better quality. In particular, it is of interest to predict the qualit y of the PhD program based on six (6) academic characteristics which are listed as follow s: SFACULTY : size in terms of the number of faculty members in t he program in 1980 (3-levels) NGRADS : number of program graduates from 1975 through 1980 PCTSUPP : percentage of program graduates from 1975 through 1 979 who received fellowships or training grant support during their graduate education PCTGRANT : percentage of faculty members holding research gran ts from the Alcohol, Drug Abuse, and Mental Health Administration, the Nation al Institutes of Health, or the National Science Foundation at any time during 1978 through 1980 NARTICLE : number of published articles attributed to program faculty members from 1978 through 1980 PCTPUB : percentage of faculty with one or more published ar ticles from 1978 through 1980 The data are recorded in the phdpsych.xlsx data set.
Before proceeding with the model fitting procedure, represent SFACULTY first in terms of dummy variables using SFACULTY = “Small” as the baseline. Then generate the STATISTICA output for this regres sion analysis and print out the result, attach it to the yellow pad paper. 1.) On your yellow pad paper, identify the response variable in this study.
2.) On your yellow pad paper, determine the fitted mult iple linear regression equation for the variable identified in (1) using all other variable s in the dataset as predictors. Determine and interpret the coefficient of determination of this model.
3.) Which of the predictors considered are significant in the fitted model at = 1%? Justify.
4.) Interpret the dummy/indicator variable found to be significant in (3).
5.) Using the fitted model, identify which observations were OVERESTIMATED only by the model (i.e., list down the ‘ID/Subject Number’ of t hose observations according to STATISTICA).
Part III: Article Reading and Understanding Read the article entitled “Correlates of psychological mindedness ” by Trudeau and Reich (1995). In particular, focus on the discussion of the relat ionships between psychological mindedness, self- consciousness, and mental well-being. Prepare a bri ef report (no more than 250 words), typewritten on MS Word.docx, on how the multiple li near regression analytical framework was applied in the analysis of the conducted survey. Pa rticularly, focus on identifying the independent and dependent variables, the data collection proced ure, the results and assessment of the procedure (i.e., identification of significant variables, mod el assessment, etc.), and the conclusions and discussion made about the regression results in rel ation with the problem identified.
Caution: Make sure that the report you submit is your OWN re port and you did not seek the aid of anybody in writing your report. If your work fai ls the plagiarism checker test, your entire worksheet will receive a zero score. SUBMISSION DEADLINE: on or before 2:00 pm Saturday, June 17, 2017. Mathematics Department, 6/F William Hall
