[DATA] Putting It Together: Predicting Intelligence 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 12_4_19 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
d. Provide an interpretation of the intercept.

Verified step by step guidance

1. Identify the regression model used to predict intelligence (IQ) from the predictors, which likely includes perceived intelligence and possibly other variables. The model can be written as: \[\text{IQ} = \beta_0 + \beta_1 \times \text{Perceived Intelligence} + \cdots + \epsilon\] where \(\beta_0\) is the intercept.
2. Recall that the intercept \(\beta_0\) represents the expected value of the dependent variable (IQ) when all predictor variables are equal to zero. In this context, it is the predicted IQ when perceived intelligence (and any other predictors) are zero.
3. Since perceived intelligence scores are mean z-scores, a value of zero corresponds to the average perceived intelligence rating. Therefore, the intercept represents the predicted IQ for an individual whose perceived intelligence rating is average.
4. Interpret the intercept in practical terms: it gives the baseline IQ prediction for an average perceived intelligence rating, before considering the effect of perceived intelligence or other variables.
5. Note that the intercept's meaningfulness depends on whether zero is within the range of the predictor variables and the context of the data. Here, because z-scores are standardized, zero is a meaningful reference point.

Key Concepts

Intercept in Regression Analysis

The intercept is the predicted value of the dependent variable when all independent variables are zero. It represents the baseline level of the outcome in the absence of predictors. Interpreting the intercept helps understand the starting point of the model before considering other factors.

Z-Score Standardization

Z-score standardization transforms data to have a mean of zero and a standard deviation of one. This process removes individual biases by putting ratings on a common scale, allowing fair comparison across raters. It is essential for aggregating subjective ratings like perceived intelligence.

Mean as a Measure of Central Tendency

The mean is the average value of a set of numbers, calculated by summing all values and dividing by their count. Using the mean z-score aggregates multiple raters' standardized scores into a single representative rating for each photo, summarizing overall perception.