Preparation for the Story Problem Portion of Quiz #11a. Tell how to interpret each of the following correlations+ r for a quantitative (continuous) predictor variablensig r for a quantitative (continuous) predictor variable-r for a quantitative (continuous) predictor variable+ r for a binary predictor variablensig r for a binary predictor variable-r for a binary predictor variableb. Tell how to interpret each of the following simple regression weights+ b for a quantitative (continuous) predictor variablensig b for a quantitative (continuous) predictor variable-b for a quantitative (continuous) predictor variable+ b for a binary predictor variablensig b for a binary predictor variable-b for a binary predictor variablec. Tell how to interpret each of the following multiple regression weights+ b for a quantitative (continuous) predictor variablensig b for a quantitative (continuous) predictor variable-b for a quantitative (continuous) predictor variable+ b for a binary predictor variablensig b for a binary predictor variable-b for a binary predictor variabled. When one considers the correlation of a specific predictor with the criterion and that predictor's contribution to a multiple regression, there are nine possibilities. Specify each of them (there might be a "special name" or maybe just a description. Correlation Multiple Regression significant - non-significant significant + Weightsignificant - non-significant significant +Answers 1a. interpreting correlationsquant predictors+r direct relationship -- those with higher scores on the predictor tend to have higher scores on the criterion (and vice versa)nsig r no reliable relationship between pred and crit -- knowing value of one tells you nothing about value of the other-r indirect relationship -- those with higher scores on the predictor tend to have lower scores on the criterion (and vice versa)binary predictors+r group with higher coded value has higher mean score on the criterion (and vice versa)nsig r no reliable mean difference on the criterion between the groups-r group with the higher coded value has lower mean score on the criterion (and vice versa)b. interpreting simple regression weightsquant predictors+b direct relationship -- each 1-point increase in the predictor is expected to be associated with an increase in the predicted criterion score equal to "b"nsig b no reliable prediction about the change in the predicted criterion score based on changes in that predictor, -b indirect relationship -- each 1-point increase in the predictor is expected to be associated with an decrease in the predicted criterion score equal to "b"binary predictors+b group with higher coded value had a mean on the criterion score "b" higher than the group with the lower coded scorensig b no reliable mean difference on the criterion between the groups-b group with higher coded value had a mean on the criterion score "b" lower than the group with the lower coded scorec. interpreting multiple regression weightsquant predictors+b direct relationship -- each 1-point increase in the predictor is expected to be associated with an increase in the predicted criterion score equal to "b", if the values of the other predictors are held constant (controlled for) (and vice versa)nsig b no reliable prediction about the change in the predicted criterion score based on changes in that predictor, ", if the values of the other predictors are held constant (controlled for) (and vice versa)-b indirect relationship -- each 1-point increase in the predictor is expected to be associated with an decrease in the predicted criterion score equal to "b", if the values of the other predictors are held constant (controlled for) (and vice versa)binary predictors+b group with higher coded value had a mean on the criterion score "b" higher than the group with the lower coded score, if the values of the other predictors are held constant (controlled for) (and vice versa)nsig b no reliable mean difference on the criterion between the groups, if the values of the other predictors are held constant (controlled for) -b group with higher coded value had a mean on the criterion score "b" lower than the group with the lower coded score, if the values of the other predictors are held constant (controlled for) (and vice versa)Considering correlations and regression weights Correlation Multiple Regression significant - non-significant significant + Weightsignificant - *** !!! !!! non-significant ^^^ boring variable ^^^significant + !!! !!! ****** good correlate & direct contributor ^^^ good correlate, but collinear with other predictors !!! Supressor variablePractice #1Correlations.357 .013 .826 -.354.035 .891 .000 .036120 120 120 120Pearson CorrelationSig. (2-tailed)NRATING2AGE GENDER SALARY NFRNDSa. Should I be concerned about the statistical power involved in the gender correlation? Carefully explain your answer. If so, what is the probability of a Type II error for this analysis?b. Should I be concerned about the statistical power involved in the age? Carefully explain your answer. If so, what is the probability of a Type II error for this analysis?c. We are planning to replicate this study and want to be 90% confident we will get significant results for any correlation as large as .30. What sample size should we use?d. Consider this SPSS output. Tell the upper and lower outlier bounds. Are there any outliers? What would be the likely result of "cleaning" these outliers upon the mean, std and skewness?Descriptives36822.496105.97233198.0050432.002.039MeanStd. DeviationMinimumMaximumSkewnesssalaryStatisticPercentiles32216.00 36441.00 41427.0032391.00 36441.00 41362.00salarysalaryWeightedAverage(Definition 1)Tukey's Hinges25 50 75PercentilesCorrelations.357 .013 .826 -.354.035 .891 .000 .036120 120 120 120Pearson CorrelationSig. (2-tailed)NRATING2AGE GENDER SALARY NFRNDSModel Summary.828a.685 .674 2.28317Model1R R SquareAdjustedR SquareStd. Error ofthe EstimatePredictors: (Constant), NFRNDS, SALARY, AGE,GENDERa. a. What are the viable individual predictors?b. Interpret the simple correlation of age.ANOVAb1304.528 4 326.132 62.563