Climate scientists have been observing the extent of sea ice in the northern Arctic using satellite observations. Many have expressed concern because in recent decades the extent of sea ice has declined precipitously—possibly due to global climate change. Here is an analysis relating the minimum (September) Extent of sea ice (km2) to the Mean Global Temperature (°C) for the years 1979–2015:

a) Explain in context what the regression says.
b) Check the assumptions and conditions for regression inference.
c) The output reports s = 0.68295. Explain what that means in this context.
d) What’s the value of the standard error of the slope of the regression line?
e) Explain what that means in this context.
f) Does this analysis prove that global temperature changes are causing sea ice to melt?

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Response variable is: Extent R squared = 62.4% s = 0.6829 with 37 - 2 = 35 degrees of freedom Coefficient 73.7928 -4.42138 Variable Intercept Mean global temp Extent 7 6 LO 4 + 14.9 SE(Coeff) t-ratio 8.856 8.33 0.5806 -7.62 15.1 15.3 15.5 Mean Global Temperature °C P-value <0.0001 <0.0001