Question

A study was conducted in which participants looked at photographs of various people and guessed how old each phot regression analy ographed person was. Then the amount of error in each guess was calculated, and this was used as a response variable in Here are the names of the variables used: these will be referenced in the questions below: 2. Difference between guessed age and true age (Positive errors are overestimates, i.e. guessing an age greater than true age; negative errors are underestimat True age of person in photograph rror Truth: PhotoGender: Gender of person in photograph (Female 1, Male Here are plots of Error vs. Photo Gender and Error vs. Truth 30 30 20. 20づ 10 10 :0 -35 35 459 0 0.1 02 03 04 05 0.6 0.7 08 09 5 10 15 20 25 30 35 40 45 50 55 60 65 70 PhotoGender Truth Here is regression output from three different models, all of which use Error as the response variable: Model A: RSquare 0.15001 Term Estimate Std Error t Ratlo Prob lt Model C Intercept 3.0612916 0.186006 16.46 Truth RSquare 0.18834 0,004461 -42.2200 0.18778 Term intercept Truth PhotoGender Truth.PnotoGender -0.162194 0.009975-1626 .0001 Estimate Std Error t Ratio Prob lt! 2.6676922 0.218621 12.200001 -0.143903 0.005067 -28.40 <.0001 3.6216993 0.40875 8.86 1001 Model B: RSquare 0.02083 Estimate Std Error t Ratio Prob>lt erm Intercept 2.528097 0.131381 19.24 PhotoGender 2.72433 0.185847 -14.66 0001

Answer 1

• a).

  Error = 2.6677-0.1439*Truth+3.6217*PhotoGender-0.1622* Truth* PhotoGender

  b).

  since sample size is not given, we take for 95%, t value as 1.96 ( consider as large sample).

  Confidence interval for slope : β± t*se

  Lower limit: -2.72433-1.96*0.185847 =-3.08859012

  upper limit: -2.72433+1.96*0.185847 =-2.36006988

  95% CI = ( -3.0886, -2.3601)

  c).

  95% CI for slope does not contain 0 value. Therefore slope is significantly different from 0.