The following table gives the number of miles per gallon in...

The following table gives the number of miles per gallon in the city and on the highway for some of the most fuel efficient cars according to Consumer Reports. Make a scatterplot of the data using city mileage as the predictor variable. Find the regression equation and use it to predict the highway mileage for a fuel-efficient car that gets 40 miles per gallon in city driving. Would it be appropriate to use the regression equation to predict the highway mileage for a fuel-efficient car that got 60 miles per gallon in city driving? If so, make the prediction. If not, explain why it would be inappropriate to do so. $$ \begin{array}{|lcc|} \hline \text { Model } & \text { City Mileage } & \text { Highway Mileage } \\ \hline \text { Toyota Prius 3 } & 43 & 59 \\ \hline \text { Hyundai Ioniq } & 42 & 60 \\ \hline \text { Toyota Prius Prime } & 38 & 62 \\ \hline \text { Kia Niro } & 33 & 52 \\ \hline \text { Toyota Prius C } & 37 & 48 \\ \hline \text { Chevrolet Malibu } & 33 & 49 \\ \hline \end{array} $$$$ \begin{array}{|lcc|} \hline \text { Model } & \text { City Mileage } & \text { Highway Mileage } \\ \hline \text { Ford Fusion } & 35 & 41 \\ \hline \text { Hyundai Sonata } & 31 & 46 \\ \hline \text { Toyota Camry } & 32 & 43 \\ \hline \text { Ford C-Max } & 35 & 38 \\ \hline \end{array} $$

The following table gives the number of miles per gallon in the city and on the highway for some of the most fuel efficient cars according to Consumer Reports. Make a scatterplot of the data using city mileage as the predictor variable. Find the regression equation and use it to predict the highway mileage for a fuel-efficient car that gets 40 miles per gallon in city driving. Would it be appropriate to use the regression equation to predict the highway mileage for a fuel-efficient car that got 60 miles per gallon in city driving? If so, make the prediction. If not, explain why it would be inappropriate to do so.
$$
\begin{array}{|lcc|}
\hline \text { Model } & \text { City Mileage } & \text { Highway Mileage } \\
\hline \text { Toyota Prius 3 } & 43 & 59 \\
\hline \text { Hyundai Ioniq } & 42 & 60 \\
\hline \text { Toyota Prius Prime } & 38 & 62 \\
\hline \text { Kia Niro } & 33 & 52 \\
\hline \text { Toyota Prius C } & 37 & 48 \\
\hline \text { Chevrolet Malibu } & 33 & 49 \\
\hline
\end{array}
$$$$
\begin{array}{|lcc|}
\hline \text { Model } & \text { City Mileage } & \text { Highway Mileage } \\
\hline \text { Ford Fusion } & 35 & 41 \\
\hline \text { Hyundai Sonata } & 31 & 46 \\
\hline \text { Toyota Camry } & 32 & 43 \\
\hline \text { Ford C-Max } & 35 & 38 \\
\hline
\end{array}
$$

Key Concepts

Scatterplot

A scatterplot is a type of graph used to display the relationship between two quantitative variables. Each point on the scatterplot represents an observation that has two values: one for the predictor (independent variable) and one for the response (dependent variable). This visual representation helps in identifying patterns, trends, and potential linear relationships between the variables.

Predictor and Response Variables

In regression analysis, the predictor variable (also called the independent variable) is the one used to predict or explain changes in another variable, known as the response variable (dependent variable). Understanding which variable is the predictor and which is the response is essential for setting up the analysis and interpreting the relationship accurately.

Least Squares Regression

Least squares regression is a statistical method used to determine the line that best fits a set of data points in a scatterplot. This line minimizes the sum of the squared differences between the observed values and the values predicted by the line. It provides an equation that can be used to estimate the response variable based on the predictor variable.

Regression Equation

The regression equation typically takes the form y = b0 + b1x, where b0 is the intercept and b1 is the slope. This equation summarizes the linear relationship between the predictor and the response variable, allowing for predictions of the response variable based on new values of the predictor variable.

Extrapolation

Extrapolation involves using a regression equation to make predictions about values of the response variable outside the range of the data that was used to create the model. While interpolation (predicting within the range of data) is generally more reliable, extrapolation can lead to unreliable predictions if the relationship does not hold true beyond the observed data.

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