Question

a weather historian gathered data about the average temperature and total snowfall in her city during the month of january in recent years. the scatter - plot shows the data she gathered and the line of best fit. january weather the equation of the line of best fit is $y=-0.368x + 18.5$. the correlation coefficient is - 0.9829. complete the sentences to interpret and describe the linear model. when the average temperature is $0^{circ}f$, the total snowfall is around inches. there is association between average temperature and total snowfall because the absolute value of the correlation coefficient is

Explanation:

Step1: Substitute temperature value

We are given the equation of the line of best - fit $y=-0.368x + 18.5$, where $y$ is the total snowfall and $x$ is the average temperature. When $x = 0$, we substitute $x = 0$ into the equation.
$y=-0.368\times0+18.5$

Step2: Calculate snowfall

Since $-0.368\times0 = 0$, then $y = 18.5$.
The correlation coefficient $r=-0.9829$. The absolute value of the correlation coefficient $|r|=0.9829$. Since $|r|$ is close to 1 (where $|r|\in[0,1]$), there is a strong association. The negative sign of $r$ indicates a negative association.

Answer:

When the average temperature is $0^{\circ}F$, the total snowfall is around 18.5 inches.
There is a strong negative association between average temperature and total snowfall because the absolute value of the correlation coefficient is close to 1.