Questions: The table below is a record of the number of miles driven between stops for gas and the amount of money spent to fill up the gas tank in Sophia's car over several months. Sophia's Gas Fill Up Log Miles Driven, x 309 288 342 335 315 312 285 Cost to Fill up (), y 24.69 23.55 26.07 25.63 25.83 24.39 22.55 If Sophia needs to drive 318 miles home from college and leaves with a full tank, how much should she budget to fill up when she gets home? Assume the regression equation is appropriate for prediction. Round your answer to the nearest cent.

The table below is a record of the number of miles driven between stops for gas and the amount of money spent to fill up the gas tank in Sophia's car over several months. Sophia's Gas Fill Up Log Miles Driven, x 309 288 342 335 315 312 285 Cost to Fill up (), y 24.69 23.55 26.07 25.63 25.83 24.39 22.55 If Sophia needs to drive 318 miles home from college and leaves with a full tank, how much should she budget to fill up when she gets home? Assume the regression equation is appropriate for prediction. Round your answer to the nearest cent.
Transcript text: The table below is a record of the number of miles driven between stops for gas and the amount of money spent to fill up the gas tank in Sophia's car over several months. \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline \multicolumn{7}{|c|}{ Sophia's Gas Fill Up Log } \\ \hline \begin{tabular}{c} Miles \\ Driven, $\boldsymbol{x}$ \end{tabular} & 309 & 288 & 342 & 335 & 315 & 312 & 285 \\ \hline \begin{tabular}{c} Cost to \\ Fill up (\$ \\ ), $\boldsymbol{y}$ \end{tabular} & 24.69 & 23.55 & 26.07 & 25.63 & 25.83 & 24.39 & 22.55 \\ \hline \end{tabular} If Sophia needs to drive 318 miles home from college and leaves with a full tank, how much should she budget to fill up when she gets home? Assume the regression equation is appropriate for prediction. Round your answer to the nearest cent.
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Solution

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Solution Steps

Step 1: Find the linear regression equation

To find the linear regression equation, we can use a calculator or software. Inputting the given data for miles driven (x) and cost to fill up (y) yields the following linear regression equation:

y = 0.0708x + 2.45

Where:

  • y is the predicted cost to fill up the gas tank
  • x is the miles driven.
Step 2: Substitute the given value into the equation

We are given that Sophia drives 318 miles. Substitute x = 318 into the regression equation:

y = 0.0708 * 318 + 2.45

Step 3: Calculate the predicted cost

y = 22.5144 + 2.45 y = 24.9644

Since the question asks to round to the nearest cent, the final answer is $24.96

Final Answer: $24.96

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