data <- read.table(text = "  sample methodx methody
                   1      1    0.52    0.53
                   2      2    0.50    0.51
                   3      3    0.48    0.48
                   4      4    0.40    0.41
                   5      5    0.36    0.36
                   6      6    0.30    0.32
                   7      7    0.28    0.30
                   8      8    0.28    0.29", header = T)

# Regression analysis
model <- lm(data$methodx ~ data$methody)
summary(model)

# Residuals:
#   Min        1Q     Median        3Q       Max
# -0.007317 -0.004931 -0.002012  0.004596  0.011341
#
# Coefficients:
#             Estimate Std. Error    t value  Pr(>|t|)
#  (Intercept)  -0.02341    0.01181  -1.983   0.0946 .
#  data$methody  1.03354    0.02879  35.900   3.11e-08 ***
#   ---
#   Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
# Residual standard error: 0.007374 on 6 degrees of freedom
# Multiple R-squared:  0.9954,  Adjusted R-squared:  0.9946
# F-statistic:  1289 on 1 and 6 DF,  p-value: 3.115e-08

# Paired t-test
t.test(data$methodx, data$methody, paired = TRUE)

# Paired t-test
#
# data:  data$methodx and data$methody
# t = -3.7417, df = 7, p-value = 0.007247
# alternative hypothesis: true difference in means is not equal to 0
# 95 percent confidence interval:
#   -0.016319724 -0.003680276
# sample estimates:
#   mean of the differences
#                     -0.01

x = runif(30, -5, 10)
y = jitter(1.2*x)

summary(lm(y~x))

x1 = runif(30, -5, 10)
x2 = runif(30, -5, 5)
x3 = runif(30, -5, 0)

null_model <- lm(methodx ~ offset(1*methody) -1, data=data)

anova(model, null_model)

Model 1: methodx ~ methody
Model 2: methodx ~ offset(1 * methody) - 1
  Res.Df        RSS Df   Sum of Sq      F  Pr(>F)
1      6 0.00032622
2      8 0.00120000 -2 -0.00087378 8.0355 0.02009 *