Question

Interpret slope and intercept of the regression line

Context: The City of Perpetual Misfortune has several factories that emit Patented Chemical #47 into the air. However, due to factory locations, wind, etc., the level of Patented Chemical #47 in the air varies within each 147 neighborhoods. Several researchers believe that Patented Chemical #47 may be associated with developing a lung disease known as Lung Rot.

A study measures the average maximum daily level of Patented Chemical #47, measured in parts per million (ppm) and the rate per 1,000 residents of new cases of Lung Rot in each of the 147 neighborhoods for the year 2018.

(1) The owners of the company releasing Patented Chemical #47 into the air believe that the study cited above exaggerates the health risks of Patented Chemical #47. They cite a study by some of their own researchers in the City of Perpetual Obfuscation, which calculated the regression line to be y = 3.46 - 0.21x. Interpret the intercept.

(2) The owners of the company releasing Patented Chemical #47 into the air believe that the study cited above exaggerates the health risks of Patented Chemical #47. They cite a study by some of their own researchers in the City of Perpetual Obfuscation, which calculated the regression line to be y = 3.46 - 0.21x. Interpret the slope.

(3) Do the results of the two studies agree with each other? If not, what are the primary differences in interpretation?

Answer 1

1) Intercept represents the dependent variable when the independent variable is at initial level or equal to zero.

In the given regression equation, intercept value is 3.46, this means that when independent variable x is equal to zero, the expected value of dependent variable y is 3.46

2) Slope is the rate of change of y with respect to x.

Slope tells us how much y will change, when there is any change in x value.

In the given regression equation, slope is -0.21

Which means that for every one unit increase in independent variable x value, there will be a loss of 0.21 units in the dependent variable y.

3) No, there is a difference in both the interpretation because slope tells us about rate of change which changes based on the value of x whereas the intercept tells us about the value of y, when x is zero.

So, there is a major difference between these two interpretations.