Question

corey used the regression equation ( y = 1.505x - 88.21 ), where ( x ) is the temperature and ( y ) is the number of swimmers, to determine a possible outside temperature when 80 swimmers are at city pool.

1. ( y = 1.505(80) - 88.21 )
2. ( y = 120.4 - 88.21 )
3. ( y = 32.19 )
4. if there are 80 swimmers at the pool, the temperature is likely to be ( 32.2^{circ}f ).

analyze coreys work to find his error. what is coreys mistake?
he substituted 80 for ( x ) instead of ( y ).
he should have added 88.21 to both sides.
he should have rounded down to ( 32.1^{circ}f ).
he should have predicted about 40 swimmers when the temperature is ( 80^{circ}f ).

Explanation:

Corey's goal was to find the temperature \(x\) when the number of swimmers \(y = 80\). But in his first step \(y = 1.505(80)-88.21\), he substituted \(80\) for \(x\) instead of \(y\). The correct equation should be \(80=1.505x - 88.21\).

Answer:

He substituted 80 for \(x\) instead of \(y\).