For 20 districts, a researcher obtains r=−0.955r=-0.955r=−0.955 between an air-quality score x x\,x and respiratory-disease rate yyy. A given regression line for life expectancy z z\,z on x x\,x is z=76.8+0.703xz=76.8+0.703xz=76.8+0.703x.
Interpret rrr.
Estimate z z\,z when x=10.5x=10.5x=10.5.
Interpret the gradient of the regression line.
Explain why neither result alone proves that changing the air-quality score will change health outcomes.