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#### A bus company wanted to know if the number of complaints they received was a function of the number of buses it ran the company carried out a study comparing the average number of buses per hour for different days and the number of complaints that it received on those days the results are shown in the graph below

80 viewed last edited 6 months ago Anonymous
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#### 1. Is there an association between the variables?
2. Does the graph have a negative slope?
3. Write down the equation of the regression line. Sangeetha Pulapaka
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1. Yes, there is an association between the variables. This is because as the value of x or the number of buses per hour increases, the number of complaints decrease.
2. Yes, we have a negative slope here, negative slope means that two variables are negatively related; that is, when x increases, y decreases, and when x decreases, y increases. Graphically, a negative slope means that as the line on the line graph moves from left to right, the line falls.
3. The equation of the regression line is y = a + bx  where b is the slope of the line and a is the y-intercept. We calculate the slope of the line between two points (0,60) and (5,40) by using the slope formula \frac{y_{2}-y_{1}}{x_{2}-x_{1}}. Plugging in x_{1} = 0, y_{1}=60, x_{2}= 5, y_{2}=40, we get the slope as \frac{40-60}{5-0} = \frac{-20}{5} = -4/ The y-intercept is 60.

So plugging in these values in our equation of line we get the equation as y = -4x + 60.

Skills you may want to recall:

What is a negative slope

What is the equation of a regression line