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Ch. 10 - Correlation and Regression
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 10 - Correlation and RegressionProblem 10.2.17
Chapter 10, Problem 10.2.17

Regression and Predictions
Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10-1.


Find the regression equation, letting the first variable be the predictor (x) variable.
Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5.


Taxis Use the distance/fare data from Exercise 15 and find the best predicted fare amount for a distance of 3.10 miles. How does the result compare to the actual fare of \$15.30?

Verified step by step guidance
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Step 1: Identify the predictor (x) and response (y) variables. In this case, the distance is the predictor variable (x), and the fare is the response variable (y).
Step 2: Use the given data set from Exercise 15 to calculate the regression equation. The regression equation is typically in the form y = b0 + b1x, where b0 is the y-intercept and b1 is the slope. Use the formulas for b1 = (Σ(xi - x̄)(yi - ȳ)) / Σ(xi - x̄)^2 and b0 = ȳ - b1x̄ to compute the slope and intercept.
Step 3: Substitute the given distance of 3.10 miles into the regression equation to calculate the predicted fare. This involves replacing x in the equation y = b0 + b1x with 3.10.
Step 4: Compare the predicted fare obtained from the regression equation to the actual fare of \$15.30. Calculate the difference between the predicted and actual values to assess the accuracy of the prediction.
Step 5: Interpret the results. If the predicted fare is close to the actual fare, the regression model is performing well for this data point. If there is a significant difference, consider potential reasons such as outliers, variability in the data, or limitations of the linear model.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Regression Analysis

Regression analysis is a statistical method used to model the relationship between a dependent variable and one or more independent variables. In this context, the regression equation helps predict the fare amount based on the distance traveled. The equation typically takes the form of a linear equation, allowing for the estimation of outcomes based on input values.

Predictor and Response Variables

In regression analysis, the predictor variable (independent variable) is the one used to predict the value of another variable, known as the response variable (dependent variable). In this case, the distance traveled (3.10 miles) serves as the predictor variable, while the fare amount is the response variable that we aim to estimate using the regression equation.
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Prediction Procedure

The prediction procedure involves using the regression equation to calculate the expected value of the response variable for a given value of the predictor variable. This process includes substituting the predictor value into the regression equation to obtain the predicted fare, which can then be compared to the actual fare to assess the accuracy of the model.
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Related Practice
Textbook Question

Finding the Best Model

In Exercises 5–16, construct a scatterplot and identify the mathematical model that best fits the given data. Assume that the model is to be used only for the scope of the given data, and consider only linear, quadratic, logarithmic, exponential, and power models.

Deaths from Motor Vehicle Crashes Listed below are the numbers of deaths in the United States resulting from motor vehicle crashes. Use the best model to find the projected number of such deaths for the year 2025.

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Textbook Question

Regression and Predictions

Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10-1.


Find the regression equation, letting the first variable be the predictor (x) variable.

Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5.

Cars Sales and the Super Bowl Listed below are the annual numbers of cars sold (thousands) and the numbers of points scored in the Super Bowl that same year. What is the best predicted number of Super Bowl points in a year with sales of 8423 thousand cars? How close is the predicted number to the actual result of 37 points?


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Textbook Question

Interpreting a Computer Display

In Exercises 9–12, refer to the display obtained by using the paired data consisting of weights (pounds) and highway fuel consumption amounts (mi/gal) of the large cars included in Data Set 35 “Car Data” in Appendix B. Along with the paired weights and fuel consumption amounts, StatCrunch was also given the value of 4000 pounds to be used for predicting highway fuel consumption.

Finding a Prediction Interval For a car weighing 4000 pounds (x = 4000) identify the 95% prediction interval estimate of the highway fuel consumption. Write a statement interpreting that interval.

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Textbook Question

Appendix B Data Sets

In Exercises 29–32, use the data from Appendix B to construct a scatterplot, find the value of the linear correlation coefficient r, and find either the P-value or the critical values of r from Table A-6 using a significance level of α = 0.05. Determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.

Taxis Repeat Exercise 15 using all of the time/tip data from the 703 taxi rides listed in Data Set 32 “Taxis” from Appendix B. Compare the results to those found in Exercise 15.

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Textbook Question

Best-Fit Line


What is a residual?

In what sense is the regression line the straight line that “best” fits the points in a scatterplot?

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Textbook Question

Interpreting a Computer Display

In Exercises 9–12, refer to the display obtained by using the paired data consisting of weights (pounds) and highway fuel consumption amounts (mi/gal) of the large cars included in Data Set 35 “Car Data” in Appendix B. Along with the paired weights and fuel consumption amounts, StatCrunch was also given the value of 4000 pounds to be used for predicting highway fuel consumption.



Testing for Correlation Use the information provided in the display to determine the value of the linear correlation coefficient. Is there sufficient evidence to support a claim of a linear correlation between weights of large cars and the highway fuel consumption amounts?

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