Question

:2. A study was conducted in which participants looked at photographs of various people and guessed how old each photographed person was. Then the amount of error in each guess was calculated, and this was used as a response variable in regression analyses. Here are the names of the variables used; these will be referenced in the questions below: Error: Difference between guessed age and true age. (Positive errors are overestimates, i.e. guessing an age greater than true age; negative errors are underestimates.) True age of person in photograph Truth: PhotoGender: Gender of person in photograph (Female 1, Male 0) Here are plots of Error vs. PhotoGender and Error vs. Truth: 553 30 20 1. 30 203 10 10 10 39 -35 35 .45 45 -65 5 10 15 20 25 30 35 40 45 50 55 60 65 70 Truth 0 0.1 02 03 04 0.5 06 0.7 08 09 1 Here is regression output from three different models, all of which use Error as the response variable Model A 0.15001 RSquare Term Estimate Std Error t Ratio Prob ltl Model C: Intercept 3.0612916 0.186006 16.46 001 Truth RSquare 0.18778 -0.18834 0.004461 -42.22<0001 Estimate Std Error t Ratio Prob> lt 2.6676922 0.218621 12.20 <0001 -0.143903 0.005067 -28.40 <.0001 3.6216993 0.40875 8.86 .0001 Truth-photoGender -0.162194 0.009975-1626 -c.000 Term Intercept Truth PhotoGender Model B: 0.020831 RSquare Estimate Std Error t Ratio Prob> Itl Intercept 2.528097 0.131381 -19.24 0001 PhotoGender 2.72433 0.185847 14.66 .0001 the estimated regression equation for model C. Be sure to include the variable names where relevant. (3 points) a. Write out (2 points) Make an approximate 95% CI for the slope of the predictor variable in Model B b. In what way does the CI from part b. "agree" with its corresponding p-value? (2 points) C.

Answer 1

Answer:

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.

The result agrees the result of the p value which is less than 0.0001 which is significant.