EPS 625 – INTERMEDIATE STATISTICSBLOCK ENTRY MULTIPLE REGRESSION – EXAMPLEA researcher conducted a study to evaluate a strength-injury hypothesis. She collects data on agroup of 100 elderly women. Specifically, the study was designed with five predictor variablesdivided into lower-body strength measures (QUADRICEPS, GLUTS, and ABDOMENS) andupper-body strength measures (ARMS and GRIP). The researcher sets out to determine howaccurately can a physical INJURY index (injury, which is the number and severity of accidents)be predicted from a linear combination of five different strength measures for elderly women?Specifically, she wants to know:1. How well can a physical injury index be predicted from a linear combination ofstrength measures in elderly women?2. How well do the lower-body strength measures predict the physical injury indexfor elderly women?3. How well do the upper-body strength measures predict the physical injury indexfor elderly women?4. For elderly women, how well do the upper-body strength measures predict thephysical injury index over and above the lower-body strength measures?The dataset for this example is on the web site, labeled Injury Index (MLR) – Dataset. Thedataset contains a total of 6 variables for a sample of 100 elderly women. For this example, youwill use an a priori alpha level of .05 ( = .05) for all analyses. Your dependent measure will bethe participants’ physical injury index (INJURY), which is based on the records kept by theparticipant’s physician and the independent variables are as follows:quadriceps A measure of strength primarily associated with the quadricepsgluts A measure of strength of the muscles in the upper part of the back of the legand the buttocksabdomens A measure of strength of the muscles of the abdomen and the lower backarms A measure of strength of the muscles of the arms and the shouldersgrip An assessment of the hand-grip strengthinjury Overall injury index based on the records kept by the participant’s physicianOnce you have obtained the data set, complete/answer each of the following questions. Be brief– but be thorough in order to receive the maximum possible points for each question. Be sure toanswer all parts and sub-parts of each question.1. First, check for multicollinearity. Conduct the appropriate diagnostic analysis and indicateyour findings below. Be sure to include what you found, the criteria in which it was judgedagainst, and indicate whether there is a concern or not and how you made your decision.FOR MULTICOLLINEARITY:Checked: VARIANCE INFLATION FACTOR (VIF) Criteria (critical value): 10.0 (greater than)VARIABLE OBTAINED(INDICATED) VALUECONCERN OR NOTA CONCERNREASON FORDECISIONQUADRICEPS1.441 Not a concern VIF < 10.0GLUTS1.670 Not a concern VIF < 10.0ABDOMENS1.478 Not a concern VIF < 10.0ARMS1.410 Not a concern VIF < 10.0GRIP1.272 Not a concern VIF < 10.02. Using the full dataset – run the regression analysis to answer the following questions:1. How well can a physical injury index be predicted from a linear combination of strengthmeasures in elderly women?2. How well do the lower-body strength measures predict the physical injury index forelderly women?3. How well do the upper-body strength measures predict the physical injury index forelderly women?4. For elderly women, how well do the upper-body strength measures predict the physicalinjury index over and above the lower-body strength measures?2a. In answering the first research question, indicate what proportion of the total variance inthe injury index is explained by the entire set of independent variables? Is this proportionof explained variance significant? Indicate how you made that decision.Approximately 32.7% (r2 = .327)YES, this is significant (from the Model 2 section of the ANOVA table)F(5, 94) = 9.127, p < .001BLOCK ENTRY MLR – INJURY INDEX EXAMPLEPAGE 22b. In answering the second research question, indicate what proportion of the total variancein the injury index is explained by the set of control (lower-body strength) variables? Isthis proportion of explained variance significant? Indicate how you made that decision.Approximately 24.5% (r2 = .245)YES, this is significant (from the Model 1 section of the Model Summary, ChangeStatistics table or the Model 1 section of the ANOVA table)F(3, 96) = 10.363, p < .0012c. In answering the third and fourth research questions, indicate what proportion of the totalvariance in the physical injury index is explained by the second set (upper-body strength)of variables? Is this proportion of explained variance significant? Indicate how you madethat decision.Approximately 8.2% (r2 = .082)YES, this is significant (from the Model 2 section of the Model Summary, ChangeStatistics table)F(2, 94) = 5.738, p < .01 (or p = .004)3. Of the five independent variables, which ones (if any) have a significant influence on thedependent measure? Indicate how you made your determination (account for all 5 variables).Information can be included From Model 1:Quadriceps, t = 1.033 (Not Significant) p = .304 (or p > .05)Gluts, t = -1.633 (Not Significant) p = .106 (or p > .05)Abdomens, t = -3.944, p < .001However, the information From Model 2 is what will be used to compare all variables individually:Quadriceps, t = 1.536 (Not Significant) p = .128 (or p > .05)Gluts, t = -1.245 (Not Significant) p = .216 (or p > .05)Abdomens, t = -3.834 (Significant), p < .001 ( p < .05)Arms, t = -3.366 (Significant), p < .01 (or p = .001, or p < .05)Grip, t = 1.596 (Not Significant) p = .114 (or p > .05)BLOCK ENTRY MLR – INJURY INDEX EXAMPLEPAGE 34. List the independent variables, from greatest to least, that are of relative importance (have asignificant influence) on the dependent measure. Indicate how you made your determination.Careful on the selection.Looking at only those that were found significant (p < α)… (in order of importance – from highest to lowest):Abdomens, β = -.395Arms, β = -.338The information should be obtained from Model 2 (the full Model) in that it is where we can compare all five variables to each other…5. Choose any one of the significant independent variables (listed above in question 4) from the full model (Model 2) and briefly explain its relationship with the dependent measure.For Abdomens:β = -.395 – indicating that as the elderly women increase their abdominal strength (controlling