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Ch. 10 - Correlation and Regression
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Triola 14th EditionCh. 10 - Correlation and Regression문제 10.3.11
10장, 문제 10.3.11

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.


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Predicting Highway Fuel Consumption Using a car weight of x = 4000 (pounds), what is the single value that is the best predicted amount of highway fuel consumption?

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Identify the regression equation provided in the computer display. The regression equation typically has the form y = b0 + b1 * x, where y is the dependent variable (highway fuel consumption), x is the independent variable (car weight), b0 is the y-intercept, and b1 is the slope.
Substitute the given value of x = 4000 (pounds) into the regression equation. This means replacing x in the equation with 4000.
Simplify the equation by performing the multiplication and addition operations to calculate the predicted value of y (highway fuel consumption).
Interpret the result as the best predicted amount of highway fuel consumption for a car weight of 4000 pounds, based on the regression model.
Verify that the prediction falls within the range of observed data to ensure it is reasonable and consistent with the model's assumptions.

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주요 개념

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Linear Regression

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. In this context, highway fuel consumption is the dependent variable, while car weight is the independent variable. The goal is to find the best-fitting line that predicts fuel consumption based on weight, allowing for predictions at specific values, such as 4000 pounds.
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04:40
Calculating Correlation Coefficient - Graphing Calculator

Prediction Equation

The prediction equation in linear regression is derived from the regression line, typically expressed in the form y = mx + b, where y is the predicted value, m is the slope, x is the independent variable, and b is the y-intercept. This equation allows us to input a specific weight (e.g., 4000 pounds) to calculate the expected highway fuel consumption, providing a single predicted value.
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03:06
Intro to Random Variables & Probability Distributions Example 1

Paired Data

Paired data refers to two related sets of observations, in this case, weights of cars and their corresponding fuel consumption. Each pair consists of a weight and its associated fuel consumption, allowing for analysis of the relationship between the two variables. Understanding paired data is crucial for interpreting the results of regression analysis and making accurate predictions.
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Visualizing Qualitative vs. Quantitative Data
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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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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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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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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.

Sound Intensity The table lists intensities of sounds as multiples of a basic reference sound. A scale similar to the decibel scale is used to measure the sound intensity.

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Randomization

For Exercises 33–36, repeat the indicated exercise using the resampling method of randomization.

Powerball Jackpots and Tickets Sold Exercise 14

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Standard Error of Estimate A random sample of 118 different female statistics students is obtained and their weights are measured in kilograms and in pounds. Using the 118 paired weights (weight in kg, weight in lb), what is the value of se? For a female statistics student who weighs 100 lb, the predicted weight in kilograms is 45.4 kg. What is the 95% prediction interval?

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