Question

There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least-squares fit of some data collected by a biologist gives the model y^=25.2+3.3x , where x is the number of chirps per minute and y^ is the estimated temperature in degrees Fahrenheit. What is the predicted increase in temperature for an increase of = chirps per minute?

a. 3.3°F

b. 16.5°F

c. 25.2°F

d. 28.5°F

e. 41.7°F

Short answer

The correct option is (b)$16.5°F$

Step-by-step solution

Given information

The regression equation for least-squares

$\stackrel{⏜}{y}=25.2+3.3x$

Concept

The least-squares regression line reduces the sum of squares of vertical distances between the observed points and the line to zero.

Explanation

$$\begin{gathered} replacingxbyx+5 \\ \stackrel{⏜}{y}=25.2+3.3(x+5) \\ =(25.2+3.3x)+16.5 \end{gathered}$$

It is observed that if $x$ is increased by $5$ then the expected value $y$ increases by $16.5F$

Hence, the correct option is (b)