1· (Twelve parts; 40 marks in total) Though global climate change is partly a na

Question

1· (Twelve parts; 40 marks in total) Though global climate change is partly a natural phenomenon, it appears to be largely exacerbated and accelerated by various human activities. In particular, carbon dioxide emissions due to industries, automobiles, and deforestation may be largely responsible for the rise in global surface temperature, which in turn results in numerous other environmental consequences. Below is partial SPSS output analyzing the relationship between global atmospheric CO2 (in ppm), as a predictor variable, and the minimum summer coverage of Arctic sea ice (in millions of square kilometers), as a response variable. The analysis is based on data recorded over a 20-year period from 1998 to 2017, inclusive (fronm NOAA, an organization which has been collecting global climate data since 1880). Using the computer output provided, answer parts (a) to (k) based on the simple linear regression model, (Arctic sea ice | CO.) = ' +/(0), . Assume that all the required assumptions for this model are satisfied Descriptive Statistics Mean Std. Deviation 5.4200 Arctic sea ice CO2 8637 12.3129 384.6500 20

Explanation / Answer

Part a)

CO2=394

Coverage=3.6000

.

As per the regression model, we get the regression equation coefficients from the last output table:

Constant = 26.0189 and slope = -0.536

Thus the Predicted value of coverage is as follows for CO2=394

Predicted Coverage = 26.0189 -0.0536*394

Predicted coverage = 4.9005

.

Formula of Residual is:

Residual = Actual value – Predicted value

Residual = 3.6000 – 4.9005

Residual = -1.3005

.

Answer to part b)

Percentage of variability is explained by the term coefficient of determination ( rsquare)

The formula of r square = (SSR / SST)

We got SSR = 8.2610

SST = 14.1720

Thus , on plugging these values in the formula of R square we get:

R square = (8.2610 / 14.1720) * 100

R square = 58.2910%

This implies that the model is able to explain only 58.29% of the variation in the coverage.

.

Part c)

We got SS regression = 8.2610

SS total = 14.1720

SS residual = SS total – SS regression

SS residual = 14.1720 – 8.2610

SS residual = 5.911

.

Formula of Standard error = square root { SS residual/ (n-2)}

We got n = 20

.

On plugging the values in the formula we get

Standard error = sqrt(5.911/(20-2))

Standard error = 0.5731

.

Part d)

We got SS regression = 8.2610

Df regression = 1

[because there is only 1 independent variable]

MS regression = SS regression / df regression

MS regression = 8.2610 /1 = 8.2610

.

SS residual = 5.9110

Df residual = n-2 = 20-2 = 18

MS residual = SS residual / df residual

MS residual = 5.911 /18 = 0.3284

.

F = MS regression / MS residual

F = 8.2610/0.3284

F = 25.1553

.

For F statistic 25.1533 at df = 1, 18 , we get the P value = 0.0000897785

This we can get using the excel formula =F.DIST.RT(25.1553,1,18)

.

Inference: Since the P value < 0.05 significance level, we reject the null hypothesis

Conclusion: Thus we conclude that The coverage is dependent on the CO2 level

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