Question

annual high temperatures (celsius) in a certain location have been tracked for several years on the same date. let x represent the number of years after 2000 and y the high temperature. based on the data shown below, the linear regression equation was calculated using technology.
the equation is $hat{y}=35.437 + 0.072x$
interpret the slope:
for each additional 0.072 years, the annual high temperature will increase by 1 degree on average.
for each additional year, the annual high temperature will increase by 35.437 degrees on average.
for each additional year, the annual high temperature will increase by 0.072 degrees on average.
for each additional 35.437 years, the annual high temperature will increase by 1 degree on average.

Explanation:

In a linear regression equation of the form $\hat{y}=a + bx$, $b$ is the slope. Here, the equation is $\hat{y}=35.437 + 0.072x$, where $x$ is the number of years after 2000 and $\hat{y}$ is the high - temperature. The slope 0.072 means that for every one - unit increase in $x$ (i.e., for each additional year), the value of $\hat{y}$ (annual high temperature) increases by 0.072 on average.

Answer:

For each additional year, the annual high temperature will increase by 0.072 degrees on average.