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Interpret the least squares regression line of this data set.The manager of a ski resort in the Alps always worries there won't 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.Average temperature (in Celsius) Snow depth (in centimeters)–3 68–1 670 471 573 415 36The least squares regression line for the data set is:y=–4.269x+56.224Use it to 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.

Question

Interpret the least squares regression line of this data set.The manager of a ski resort in the Alps always worries there won't 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.Average temperature (in Celsius) Snow depth (in centimeters)–3 68–1 670 471 573 415 36The least squares regression line for the data set is:y=–4.269x+56.224Use it to 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.

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Solution

The least squares regression line equation is y = -4.269x + 56.224. This equation predicts the depth of the snow (y) based on the average temperature in January (x).

The slope of the regression line is -4.269. This means that for every one degree increase in the average temperature in January, the predicted snow depth decreases by 4.269 centimeters.

So, if the average temperature in January were one degree higher, the least squares regression line predicts there would be approximately 4.269 fewer centimeters of snow on March 1st.

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