2 Simple Regression Model Make prediction about the starting salary of a current college graduateData set of starting salaries of recent college graduatesData SetCompute Average SalaryHow certain are of this prediction?There is variability in the data.
3 Simple Regression Model Use total variation as an index of uncertainty about our predictionCompute Total VariationThe smaller the amount of total variation the more accurate (certain) will be our prediction.
4 Simple Regression Model How “explain” the variability - Perhaps it depends on the student’s GPASalaryGPA
5 Simple Regression Model Find a linear relationship between GPA and starting salaryAs GPA increases/decreases starting salary increases/decreases
6 Simple Regression Model Least Squares Method to find regression modelChoose a and b in regression model (equation) so that it minimizes the sum of the squared deviations – actual Y value minus predicted Y value (Y-hat)
7 Simple Regression Model How good is the model?a= 4,779 & b = 5,370A computer program computed these valuesu-hat is a “residual” valueThe sum of all u-hats is zeroThe sum of all u-hats squared is the total variance not explained by the model“unexplained variance” is 7,425,926
8 Simple Regression Model Total Variation = 23,000,000
9 Simple Regression Model Total Unexplained Variation = 7,425,726
10 Simple Regression Model Relative Goodness of FitSummarize the improvement in prediction using regression modelCompute R2 – coefficient of determinationRegression Model (equation) a better predictor than guessing the average salaryThe GPA is a more accurate predictor of starting salary than guessing the averageR2 is the “performance measure“ for the model.Predicted Starting Salary = 4, ,370 * GPA
18 Regression Statistics Table Multiple RR = square root of R2R2Coefficient of DeterminationR2adjused if more than one x variableStandard Error SyThis is the sample estimate of the standard deviation of the error (actual – predicted)
19 ANOVA Table Table 1 gives the F statistic Tests the claim there is no significant relationship between your all of your independent and dependent variablesThe significance F value is a p-valueshould reject the claim:Of NO significant relationship between your independent and dependent variables if p<Generally = 0.05
20 Regression Coefficients Table Coefficients Column givesb0 , b1, ,b2 , … , bn values for the regression equation.The b0 is the interceptb1value is next to your independent variable x1b2 is next to your independent variable x2.b3 is next to your independent variable x3
21 Regression Coefficients Table p values for individual t tests each independent variablest test - tests the claim that there is no relationship between the independent variable (in the corresponding row) and your dependent variable.Should reject the claimOf NO significant relationship between your independent variable (in the corresponding row) and dependent variable if p<.
27 Latent Variables Latent Variables Explanatory Variables that are not directly measuredIdentified by “Exploratory Factor Analysis”Confirmed by “Confirmatory Factor Analysis”Statistical Methods for Latent VariablesPrinciples Components AnalysisPLSSEM
28 Example: Confirmatory Factor Analysis Intention to Use Travelocity Website