Question

a scientist is interested in the relationship between the number of eggs hatched per day for frogs (y) and temperature. based on the collected data, the least-squares regression line is $hat{y}=15.66+3.58x$, where x is the number of degrees by which temperature exceeds degrees fahrenheit. which of the following statements best describes the meaning of the slope of the least-squares regression line?
for each increase of one degree fahrenheit per day, there is an estimated increase of 15.66 hatched eggs.
for each increase of one hatched egg, the estimated temperature per day increases by 15.66 degrees fahrenheit.
for each increase of one degree fahrenheit per day, there is an estimated increase of 3.58 hatched eggs.
for each increase of one hatched egg, the estimated temperature per day increases by 3.58 degrees fahrenheit.

Explanation:

The least-squares regression line is in the form $\hat{y} = a + bx$, where $b$ (the slope) represents the estimated change in $\hat{y}$ (hatched eggs) for a 1-unit increase in $x$ (temperature in degrees Fahrenheit above a baseline). Here, $b=3.58$, so each 1-degree rise in temperature corresponds to an estimated 3.58 more hatched eggs.

Answer:

For each increase of one degree Fahrenheit per day, there is an estimated increase of 3.58 hatched eggs.