Researchers at UCLA (Inagaki et al., 2016) investigated the relationship between physical warmth and social warmth. They measured physical warmth by taking oral temperatures of the 54 subjects (in degrees Celsius). To measure social warmth, they gave them a 12-item test that included questions like “I feel like being around other people.” The subjects responded on a 5-point (1 = not at all, 5 = very much so) scale for each item, and the 12 responses were averaged, giving a “warmth score” for each subject. The regression output is shown in the Exercise 10.5.25 output. 

a. Use the regression output to determine the equation of the least squares regression line. Identify all variables used in the equation. 

b. Is a linear model appropriate for these data? Explain. 

c. What is the value of the slope of the least squares regression line, and what does it mean in the context of body temperature and average social warmth score? 

d. What percentage of the variation in the warmth scores is explained by its linear relationship with body temperature? 

e. Use the regression model to predict the social warmth score for someone with a body temperature of 37°C. 

f. One of the subjects had a body temperature of 37°C and a social warmth score of 4.4. Calculate the residual for this subject and explain what it means.