Question

more crickets chirping the scatterplot shows the relationship between temperature in degrees fahrenheit (x) and chirps per minute (y) for the striped ground cricket. the equation of the regression line relating these variables is $hat{y}=-0.31 + 0.212x$. a) predict the cricket chirp rate when the temperature is 82°f. show your work. $hat{y}=-0.31 + 0.212(82)=17.074$ b) interpret the slope of the regression line. on average each °f increase in temperature was associated with | c) does the value of the y intercept have meaning in this context? if so, interpret the y intercept. if not, explain why.

Explanation:

Step1: Substitute temperature value

Given regression line $\hat{y}=- 0.31 + 0.212x$, substitute $x = 82$.
$\hat{y}=-0.31+0.212\times82$

Step2: Calculate the result

First, calculate $0.212\times82 = 17.384$. Then, $\hat{y}=-0.31 + 17.384=17.074$.

For part b:
The slope of the regression line is $0.212$. This means that on average, for each 1 - degree Fahrenheit increase in temperature, the number of cricket chirps per minute increases by $0.212$.

For part c:
The y - intercept is $-0.31$. In this context, it does not have a meaningful interpretation. The regression line is based on the observed data in the range of temperatures shown (around 70 - 95°F). A temperature of $x = 0$ is outside the range of the data used to create the regression model, and it is not physically possible to have a negative number of cricket chirps per minute.

Answer:

a) 17.074
b) On average, for each 1 - degree Fahrenheit increase in temperature, the number of cricket chirps per minute increases by 0.212.
c) No. The regression line is based on data in the range of 70 - 95°F. A temperature of 0°F is outside the data - range and a negative number of chirps per minute is not physically possible.