Data From Rstudio: Call: lm(formula = usurf ~ wlevel) Residuals: Min 1Q Median 3

Question

Data From Rstudio:

Call:
lm(formula = usurf ~ wlevel)

Residuals:
Min 1Q Median 3Q Max
-1.87181 -0.49460 0.05222 0.49831 1.31556

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.03403 0.01391 2.447 0.0145 *
wlevel -0.36007 0.01745 -20.637 <2e-16 ***
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.5842 on 1763 degrees of freedom
Multiple R-squared: 0.1946,   Adjusted R-squared: 0.1941
F-statistic: 425.9 on 1 and 1763 DF, p-value: < 2.2e-16

Please just give answer based on data/model provided, thanks

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

9)
a) the purpose of fitting this relation is to predict sea surface elevation by using surface velocity

b)
y^ = 0.03403 -0.36007 *x
or
surface elevation^ = 0.03403 -0.36007 * surface velocity

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