Question

The scatterplot below shows the relationship between the distance in miles an airplane flies from Baltimore, Maryland and the cost of an airfare in dollars. Based on this scatterplot, which of the following would best represent the cost of an airfare to a destination that is 1,300 miles from Baltimore? LOWEST-TRICED AIRFARES FROM BALTIMORE

Answer 1

In order to calculate the best airfare for 1300 miles, we need to fit a line to represent these points using linear regression.

The line can be calculated using the following equations:

`\begin{gathered} f=\hat{\alpha}+\hat{\beta}x \\ \hat{\beta}=\frac{\sum ^n_(i=1)(x_i-\bar{x})(y_i-\bar{y})}{\sum ^n_(i=1)(x_i-\bar{x})^2} \\ \hat{\alpha}=\bar{y}-\hat{\beta}\bar{x} \end{gathered}`

Calculating the average value of x and y, we have:

`\begin{gathered} \bar{x}=(170+370+410+590+610+720+940+1210+1500)/(9)\approx724 \\ \bar{y}=(108+125+160+162+144+180+180+260+215)/(9)\approx170 \end{gathered}`

Now, calculating the value of Beta, we have:

Calculating Alpha, we have:

`\hat{\alpha}=170-0.01319\cdot724=160.45`

So our function is:

`f=160.45+0.01319x`

Using the value of x = 1300, we have:

`\begin{gathered} f=160.45+0.01319\cdot1300 \\ f=177.6 \end{gathered}`

So the value that best represent the cost is $180, therefore the answer is the first option.