Question
Here is the data from Rstudio:
> # Compute the Pearson's correlation between the clay contents of the
> # topsoil and subsoil. Test whether this correlation is significant.
> sum((u .... [TRUNCATED]
[1] -0.228853
> cov(wlevel,usurf)
[1] -0.228853
> sd(wlevel); sd(usurf)
[1] 0.797231
[1] 0.6507819
> cov(wlevel,usurf)/(sd(wlevel)*sd(usurf))
[1] -0.4410999
> cor(wlevel,usurf)
[1] -0.4410999
> cor.test(wlevel,usurf)
Pearson's product-moment correlation
data: wlevel and usurf
t = -20.637, df = 1763, p-value < 2.2e-16
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
-0.4779221 -0.4027301
sample estimates:
cor
-0.4410999
ie Sulace velocity. Does Dutlons ur the sea surface imply for the underlying natural process? Comment on the differences between the sea surface elevation and the surface velocity distributions. elevation the distribution look normal or lognormal? What does this 8. Compute the Pearson's correlation between the the sea surface elevation and the surface velocity. Test whether this correlation is significant. (a) According to this test, what is the probability that the sea surface elevation and the surface velocity, in the population from which this sample was taken, are in fact not correlated? (b) What is the best estimate for the population correlation coefficient? With only 5% probability of being wrong, what are the lowest and highest values this coefficient could in fact have? 9. Fit a least-squares prediction line of the sea surface elevation as predicted by the surface velocity; write the model summary. (a) What is the purpose of fitting this relation? (b ) What is the linear least-squares relation between the sea surface elevation and the surface velocity? (c) Prepare a scatterplot with the best-fit line superimposed. Mark the centroid (centre of gravity) shown as large diamond and display two dashed lines, one a vertical line and one horizontal at the means of the two variables. 10. Compute the predicted surface velocity for each observation, and compare it graphically with the observed surface velocity (a) Prepare a plot showing the residuals plotted against predicted values, along with hori- t 3 ±2, ±1 standard deviations of the residuals.
Explanation / Answer
a)
P- value of correleation test is less than 0.05.
So the correleation is significant.
b)
Confidence interval of correleation at 95% confidence is
-0.4779221 -0.4027301
c)
Best estimate for population correleation is
-0.4410999