Question

question 15 (multiple choice worth 10 points) a scientist is interested in the relationship between the number of eggs hatched per day for frogs (y) and temperature, where x is the number of degrees by which temperature exceeds 60 degrees fahrenheit. which of the following statements best describes the meaning of the slope of the least - squares regression line? based on the collected data, the least - squares regression line is y = 15.66+3.58x. 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:

Step1: Identify regression equation form

The least-squares regression line is given as $\hat{y}=15.66+3.58x$, where $\hat{y}$ is the number of hatched eggs per day, and $x$ is the temperature above 60°F.

Step2: Interpret the slope

In a linear regression model $\hat{y}=b_0+b_1x$, the slope $b_1$ represents the change in $\hat{y}$ for a 1-unit increase in $x$. Here, $b_1=3.58$, so a 1-unit increase in $x$ (1°F above 60°F) leads to a 3.58 increase in $\hat{y}$ (hatched eggs per day).

Answer:

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