Statistical Analysis of Population and Glacier Retreat

Extract

[...] 3-b We reuse the linear model to estimate the population of India in 2011: The year 2011 corresponds to the rank: x=7 From which the prediction: y = 121.4 + 211.2 = 1061 One can predict for 2011 in India a population of 1061 million inhabitants 4-a A power adjustment could also have been considered. 4-b We plot the scatter plot on a log-log scale The points are not aligned, there is no power correlation between y and x. A power adjustment would therefore not be suitable for our data. [...]

[...] A-4 To answer this question it is enough to use the 'least squares' line obtained. The year 2020 corresponds to the rank: x=120 From which the prediction: y = 0.023 * 120 - 0.162 = 2.598 One can predict for 2020 a retreat of 2.598 km of the glacier. Its length would then be approximately 23km Now we want to determine its year of disappearance following this model. 0.023x - 0.162 = 25.6 ssi x = (25.6+ 0.162) /0.023=1120.086 So 1121 years after 1900 the glacier would disappear. [...]

[...] So let it be in the year 2607 D The exponential model seems the most adapted given the estimated dates of glacier disappearance by scientists that can be read in the press. [...]

[...] C-4 To answer this question it is enough to use the exponential adjustment obtained. The year 2020 corresponds to the rank: x=120 From which the prediction: y = 0.00595683242* 120^1.27511894872 = 2.66820250266 One can predict for 2020 a retreat of 2.668 km of the glacier. Its length would then be approximately 22km One wants to determine its year of disappearance following this model. 0.00595683242 x^1.27511894872 = 25.6 ssi x = (25.6/0.00595683242) ^ (1/1.27511894872) = 706.841575041 So 707 years after 1900 the glacier disappeared. [...]

[...] We can therefore use it as a prediction model. 1-c Determination of the linear adjustment line y = ax + b with: a = 242.8 / 2 = 121.4 b = 575.4 - 121.4*3 = 211.2 The regression line is the line of equation y = 121.4x + 211.2 1-d To answer this question it is enough to use the line of the 'least squares' obtained. The year 2001 corresponds to the rank: x=6 From which the prediction: y = 121.4 + 211.2 = 939.6 One can predict for 2001 in India a population of 939.6 million inhabitants 2-a Calculation Table X Z x^2 z^2 xz 1 5,88887796 1 34,6788836 5,88887796 2 6,08449941 4 37,0211331 12,1689988 3 6,30627529 9 39,769108 18,9188259 4 6,52649486 16 42,5951352 26,1059794 5 6,74051936 25 45,4346012 33,7025968 Sum 15 31,5466669 55 199,498861 96,7852789 Mean of 31.547/5 = 6,30933338 = 199.498861/5 - 6.30933338^2 = 0.0920845 Cov(x,z) = 96,7852789/5 - 3*6,30933338= 0.42905564 R = 0.42905564/sqrt (2*0.0920845) = 0.99978208458 The linear adjustment is of excellent quality. [...]