Question

3. All else being equal, one would expect the energy consumption to be related to the amount of CO₂ emissions. The energy consumption of buildings per unit area per unit time is measured as energy use intensity given in MJ/ft²/year. The CO2 emissions are measured in metric tons per capita per year (T/person/year). The data on the building energy consumption and CO₂ emissions values for a sample of 15 zip-codes is shown in the table below

          a.    Find the 95% confidence interval for the correlation between emissions and energy consumption.

          b.    Find the p-value for testing ?₀: ? ≤ 0.2 versus ?₁: ? > 0.2.

          c.    If the units for energy consumption were changed from MJ/ft²/year to BTU/m²/year, what is

                 the new 95% confidence interval? Note that 1 MJ is approximately 947.8 BTU and 1 foot is

         approximately equal to 0.3048 m.

          d.    Compute the least-squares line for predicting the emissions from energy consumption.

                 What are the units of the estimated slope? What are the units of the estimated intercept?

          e.    Which point has the largest magnitude of the residual?

          f.    Report the Total Sum of Squares (TSS), error sum of squares (ESS), and regression sum of

                squares (RSS). What proportion of the variation in emissions is explained by energy

                consumption?

          g.   If the energy consumption increases by 1 MJ/ft²/year, by how much would you predict the

                emissions to increase or decrease?

Energy (MJ/ft2/year)	Emissions (T/person/year)
133.3	8
154.9	11
154.1	9.1
137.1	7.3
145.4	9.7
145.8	7.2
211.1	10.3
112.1	6.5
164.2	10.8
165.4	8.7
159.7	9.2
108.4	10
161.1	7.9
130.1	7.9
117.3	9.8

Answer 1