I'm doing research into the relationships between physical features of audio signals and the perceptual responses to these signals. For example, the data below contains the "Naturalness of Timbre" ratings reported by three subjects in response to four different audio signals.
data <- data.frame( Signal=c('S1', 'S1', 'S1', 'S1', 'S1', 'S1', 'S1', 'S1', 'S1', 'S2','S2', 'S2', 'S2', 'S2', 'S2', 'S2', 'S2', 'S2', 'S3', 'S3', 'S3', 'S3', 'S3', 'S3', 'S3', 'S3', 'S3', 'S4', 'S4', 'S4','S4', 'S4', 'S4', 'S4', 'S4', 'S4'), NaturalnessOfTimbre=c(0.78338906,0.88641009,1.06669688,0.95402992,0.90072169,0.99965679,1.04912434,0.95402992,0.95402992,0.52583649,0.80914432,0.90072169,0.85125413,0.98943111,0.68608960,0.71044781,0.75231903,0.73480602,-0.24682121,-0.50910356,-0.32408698,-0.11804493,0.02841791,-0.68224000,-0.33596713,-0.28823883,-0.28823883,-1.48307353,-1.43156302,-1.35005196,-1.22638307,-1.35005196,-1.45731828,-1.48179115,-1.48179115,-1.48179115), SpectralSlope=c(11.35967,11.35967,11.35967,11.35967,11.35967,11.35967,11.35967,11.35967,11.35967,11.38028,11.38028,11.38028,11.38028,11.38028,11.38028,11.38028,11.38028,11.38028,11.32053,11.32053,11.32053,11.32053,11.32053,11.32053,11.32053,11.32053,11.32053,11.08847,11.08847,11.08847,11.08847,11.08847,11.08847,11.08847,11.08847,11.08847), Repetition=c(1,2,3,1,1,2,3,2,3,1,2,1,2,3,1,2,3,3,1,1,2,3,1,2,3,2,3,1,2,1,2,3,3,1,2,3), Subject=c(1,1,1,3,2,2,2,3,3,1,1,2,2,1,3,3,2,3,1,2,1,1,3,2,2,3,3,1,1,2,2,2,1,3,3,3) ) ggplot(data,aes_string(y='NaturalnessOfTimbre',x='SpectralSlope')) + geom_point(aes(shape=Signal,colour=Signal)) + geom_smooth(method=lm)
I'd like to report on the relationship between the feature "SpectralSlope" and the reported "Naturalness" values. I'm considering doing this using a simple linear regression model. This gives me a $\beta_1$ estimate of $7.5563$ and a very low p value ($p < 0.001$).
My question: in this case, is a simple linear regression, as above, the appropriate way to investigate the relationship? Is the analysis I've done reasonable? I'm concerned because most textbook examples that I see of linear regression have evenly spaced explanatory variables (e.g. SpecSlope of [1,2,3,4]), rather than unevenly spaced ones. Is this method still applicable when the variables aren't evenly spaced, as in my data?