I am trying to find shellfish densities for a field-based aquaculture program and wanted to understand the impact of reef structure and site on the response. This experiment only has a sample size of 36. I looked at the distribution and log-transformed it for normality before running a linear model:
model<-lm(data$logged ~ data$reef + data$site)
My output looks like this:
Estimate Std. Error t value Pr(>|t|) (Intercept) 10.2593 0.1599 64.179 < 2e-16 *** data$reef2 -1.2147 0.1958 -6.204 1.06e-06 *** data$reef3 -1.4936 0.1958 -7.629 2.61e-08 *** data$reef4 -2.6405 0.1958 -13.487 9.03e-14 *** data$reef5 -1.0867 0.1958 -5.550 6.18e-06 *** data$reef6 -0.8922 0.1958 -4.557 9.30e-05 *** data$siteB -0.6314 0.1384 -4.561 9.21e-05 *** data$siteC 0.2567 0.1384 1.854 0.0743 . Residual standard error: 0.3391 on 28 degrees of freedom Multiple R-squared: 0.8943, Adjusted R-squared: 0.8679 F-statistic: 33.85 on 7 and 28 DF, p-value: 4.937e-12
What I don't understand is why my SE value are the same for all of my coefficients. Can someone help me understand how to fix this issue?