Answer
a) $y=0.122x+2.07$
$r≈0.87$
b) See first graph
c) Italy, Japan, Canada
d) $y=0.142x-1.662$
$r\approx 0.968$
See second graph
Work Step by Step
a) Step 1:
Let 𝑥 be the per capita energy consumption (in millions of Btu) and
𝑦 be the per capita gross national income (in thousands of U.S. dollars) of a country so that the given data points are (𝑥,𝑦).
Step 2
In a graphing utility (TI), enter the 𝑥-coordinates in L1 and the y-coordinates in L2 then use the LinReg feature to find the linear model for the data. If the correlation coefficient does not appear, go to 2nd → CATALOG → DiagnosticOn for it to show.
Doing so, the linear model is
$𝑦=0.122𝑥+2.07$
and the correlation coefficient is
$r≈0.87$
b) See first graph
C) The countries that differ most from the linear model are those whose plot in the graph are far from the linear model:
Italy, Japan, Canada
d) The new linear model is:
$y=0.142x-1.662$
The correlation coefficient increases to
$r\approx 0.968$
See second graph.
