(a) Run the program exercise5_P2.R as you were instructed to do in class and in section. scatter plot of the SON Darwin rainfall anomalies versus the SON Nino3.4 Index called "exercise5_plot3.jpg." On your own personal copy of this figure, divide the plot into four quadrants centered at the origin (0,0), and label them according to "above average rainfall," "below average rainfall," "El Nio," and "La Nia" as appropriate. (6 points) (b) If we denote the Darwin SON rainfall anomaly as P and the SON Nino3.4 Index as T , then we can compute the least-squares best fit straight line that passes through all of the pairs of points (,) P T in figure exercise5_plot3.jpg. Specifically, we are looking for the straight line given by: P mT c = + (3) where m is the gradient of the line and c is the intercept (i.e. the value of P when T = 0 ). The least-squares best fit straight line computed by R is also shown in figure exercise5_plot3.jpg. Estimate directly from exercise5_plot3.jpg the values of m and c and record them on your own personal copy of the figure. (2 points) 6 (c) Using the R command summary(Darwin), record in the appropriate format on exercise5_plot3.jpg the standard deviation of the error in your estimate of the gradient of the straight line (see the green box in Fig. 1). (2 points) (d) Express from part (c) as a percentage of your estimate of m in part (b) and record on exercise5_plot3.jpg. (1 point) (e) Using the R command summary(Darwin), record the coefficient of determination 2 r on exercise5_plot3.jpg (see the red box in Fig. 1). (1 point) (f) Based on the value on the coefficient of determination from part (e), compute the correlation between Darwin precipitation P and the Nino3.4 Index T , paying particular attention to the sign of the correlation implied by Fig. 3 and the gradient of the line m in equation (3). (1 point) (g) There is a lot of scatter in the data plotted in exercise5_plot3.jpg, which is also reflected in the relatively low 2 r you found in part (e) and the relatively large percentage of error in m in part (d). Therefore it is helpful to see how the rainfall at other locations correlates with the Nino3.4 Index. Figure 4 shows a map of the correlation of SON rainfall anomalies everywhere at the earth surface with the SON Nino3.4 Index. (1 point) Carefully draw on your own copy of Fig. 4 the location of the region that defines the Nino3.4 Index. Figure 4: A map of the correlation between the SON average rainfall anomaly at points all over the earth surface with the SON averaged Nino3.4 Index. The correlations are multiplied by 100 and expressed as a percentage. From the NOAA Climate Prediction Center: http://www.cpc.ncep.noaa.gov/products/precip/CWlink/ENSO/regressions. 7 (h) Multiply the correlation coefficient that you computed in part (f) by 100% and compare it with the value at Darwin in Fig. 4. (2 points) (i) Indicate on your own copy of Fig. 4 the area of below average rainfall that is associated with the eastward migration of the rising branch of the Walker circulation during El Nio conditions. You may find the schematic in Fig. 5 helpful which is the underlying physical connection between Darwin rainfall and ENSO on which we can base a meaningful scientific hypothesis for testing equation (3). (1 point)

Call:

lm(formula = y ~ x, data = dummy)

Residuals:

Min1QMedian3QMax

-1.9674 -0.7335 -0.06310.58963.1826

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -1.212e-061.385e-010.0001

x-6.630e-011.481e-01-4.4783.3e-05 ***

---

Signif. codes:0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.108 on 62 degrees of freedom

Multiple R-squared:0.2444,Adjusted R-squared:0.2322

F-statistic: 20.05 on 1 and 62 DF,p-value: 3.295e-05