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. x y 2 31.52 3 34.43 4 34.54 5 35.15 6 35.56 7 33.27 8 35.78 9 35.69 10 33.5 11 33.21 12 32.92 13 33.23 14 36.34 the equation is $hat{y}=33.849 + 0.049x$. interpret the slope: for each additional 0.049 years, the annual high temperature will increase by 1 degree on average. for each additional 33.849 years, the annual high temperature will increase by 1 degree on average. for each additional year, the annual high temperature will increase by 33.849 degrees on average. for each additional year, the annual high temperature will increase by 0.049 degrees on average.

Explanation:

In a linear regression equation $\hat{y}=a + bx$, the slope $b$ represents the change in the dependent variable ($y$, annual high - temperature here) for a one - unit change in the independent variable ($x$, number of years after 2000 here). In the equation $\hat{y}=33.849 + 0.049x$, the slope is 0.049. This means for each additional year (one - unit increase in $x$), the annual high temperature ($y$) will increase by 0.049 degrees on average.

Answer:

For each additional year, the annual high temperature will increase by 0.049 degrees on average.