Can a photograph of an individual be used to predict their intelligence? Researchers at Charles University in Prague, Czech Republic, had 160 raters analyze the photos of 80 students and asked each rater to rate the intelligence and attractiveness of the individual in the photo on a scale from one to seven. To eliminate individual bias in ratings, each rater's scores were converted to z-scores using each individual's mean rating. The perceived intelligence and attractiveness of each photo was calculated as the mean z-score. Go to www.pearsonhighered.com/sullivanstats to obtain the data file 14_2_17 using the file format of your choice. The following explains the variables in the data: sex: Gender of the individual in the photo age: Age of the individual in the photo perceived intelligence (ALL): Mean z-score of the perceived intelligence of all 160 raters perceived intelligence (WOMEN): Mean z-score of the perceived intelligence of the female raters perceived intelligence (MEN): Mean z-score of the
perceived intelligence of the male raters attractiveness (ALL): Mean z-score of the attractiveness
rating of all 160 raters attractiveness (MEN): Mean z-score of the attractiveness rating of the male raters attractiveness (WOMEN): Mean z-score of the attractiveness rating of the female raters IQ: Intelligence quotient based on the Czech version of Intelligence Structure Test Source: leisner K, Chvátalová V, Flegr J (2014) Perceived Intelligence Is Associated with Measured Intelligence in Men but Not Women. PLoS One 9(3): e81237. doi:10.1371/journal.pone.0081237
(a) Are attractive people perceived as more intelligent? Draw a scatter diagram between attractiveness (ALL) and perceived intelligence (ALL) for all 160 raters treating perceived intelligence as the response variable.
(b) What is the linear correlation coefficient between attractiveness and perceived intelligence for all 160 raters? Based on the linear correlation coefficient, does a linear relation exist between attractiveness and perceived intelligence?
(c) Treating perceived intelligence (ALL) as the response variable and attractiveness (ALL) as the explanatory variable, find the least-squares regression equation between these two variables.
(d) Provide an interpretation of the intercept.
(e) A normal probability plot confirms the residuals are normally distributed. Test whether a positive linear relation exists between perceived intelligence and attractiveness.
(f) Are higher IQs associated with higher perceived intelligence? Draw a scatter diagram between IQ and perceived intelligence for all 160 raters treating IQ as the response variable. hat is the linear correlation coefficient between IQ and perceived intelligence (ALL)? Is this linear correlation coefficient suggestive of a linear relation between the two variables? Explain.
(g) Treating IQ as the response variable, find the least-squares regression between IQ and perceived intelligence (ALL) for females only (sex = F). Test whether a positive linear relation exists between perceived intelligence for females only and IQ. Use an α = 0.1 level of significance.
(h) Treating IQ as the response variable, find the least-squares regression between IQ and perceived intelligence (ALL) for males only (sex = M). Test whether a positive linear relation exists between perceived intelligence for males only and IQ. Use an α = 0.1 level of significance.
(i) Construct a 95% confidence interval for the mean IQ of males who have perceived intelligence of 1.28.
(j) Construct a 95% prediction interval for the IQ of a male
whose perceived intelligence is 1.28.