Researchers studying pleasant touch sensations measured the firing frequency (impulses per second) of nerves that were stimulated by a light brushing stroke on the forearm and also recorded the subject's numerical rating of how pleasant the sensation was. The accompanying data was read from a graph in the paper "Coding of Pleasant Touch by Unmyelinated Afferents in Humans" (Nature Neuroscience, April 12, 2009) .

Flrlng anoncy PW Rating 23 I 0.2 I 24 l 1 .0 1 .2 1 .2 2? l 1 .0 2.0 2.3 2.2 2.4 988523 2.8 (a) What is the equation of the estimated regression line? (b) What is the estimated average change in pleasantness rating associated with an increase of 1 impulse per second in ring frequency? (that is estimate slope b). (c) What pleasantness rating would be predicted when ring frequency was 30 impulse per second? ((1) Should this regression model be used to predict pleasantness rating when ring frequency was 80 impulse per second? Explain. (e) Calculate and interpret the value of r2. (f) Calculate and interpret the value of 3.3. (g) Estimate the mean change in pleasantness rating associated with an increase of 1 impulse per second in ring frequency using a 95% condence interval. Interpret the resulting interval. (condence interval for the slope) (h) Carry out a hypothesis test to decide if there is convincing evidence of a useful linear relationship between ring frequency and pleasantness rating (i) Construct a standardized residual plot. Does the plot exhibit any unusual features