Question

read the following description of a data set. the manager of a ski resort in the alps always worries there wont be enough snow to keep the resort open into the spring. she decided to see if there was a relationship between the temperature in january and the amount of snow in the spring. for several years, she recorded the average temperature in january (in celsius), x. on march 1, she also measured the depth of the snow at the bottom of a particular ski slope (in centimeters), y. the least squares regression line of this data set is: y = -0.463x + 31.361. complete the following sentence: if the average temperature in january were one degree higher, the least squares regression line predicts there would be fewer centimeters of snow on march 1st.

Explanation:

Step1: Identify the regression - line equation

The regression line is $y=-0.463x + 31.361$, where $y$ is the snow - depth and $x$ is the temperature.

Step2: Analyze the slope

The slope of the regression line is $m=-0.463$. This means that for every 1 - degree increase in temperature ($x$), the value of $y$ (snow - depth) changes by the value of the slope.

Step3: Calculate the change in snow - depth

If the temperature is 1 degree higher, we substitute $\Delta x = 1$ into the equation. The change in $y$ is $\Delta y=m\times\Delta x$. Since $m=-0.463$ and $\Delta x = 1$, then $\Delta y=-0.463\times1=- 0.463$.

Answer:

0.463