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Ch. 10 - Correlation and Regression
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoTriola 14th EditionCh. 10 - Correlation and RegressionProblema 10.RE.3c
Capitolo 10, Problema 10.RE.3c

Time and Motion In a physics experiment at Doane College, a soccer ball was thrown upward from the bed of a moving truck. The table below lists the time (sec) that has lapsed from the throw and the corresponding height (m) of the soccer ball.
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c. What horrible mistake would be easy to make if the analysis is conducted without a scatterplot?

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Understand the context of the problem: The question is asking about a potential mistake that could occur if the analysis is conducted without using a scatterplot. A scatterplot is a graphical representation of data points, which helps visualize relationships or patterns between variables.
Recognize the role of a scatterplot: A scatterplot is particularly useful in identifying trends, outliers, or non-linear relationships in the data. Without it, one might incorrectly assume a specific type of relationship (e.g., linear) between the variables.
Consider the nature of the data: In this case, the data involves time and height of a soccer ball. The height of the ball is likely to follow a parabolic trajectory due to the effects of gravity, which is a non-linear relationship.
Identify the potential mistake: If the analysis is conducted without a scatterplot, one might mistakenly assume a linear relationship between time and height. This could lead to incorrect conclusions or an inappropriate model being applied to the data.
Conclude the importance of visualization: Emphasize that creating a scatterplot is a critical step in data analysis to ensure that the correct relationship between variables is identified and to avoid making assumptions that could lead to errors in interpretation.

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Scatterplot

A scatterplot is a graphical representation that displays values for typically two variables for a set of data. Each point on the plot corresponds to an observation in the dataset, allowing for visual assessment of relationships, trends, and potential outliers. In the context of the soccer ball experiment, a scatterplot would help visualize how height changes over time, making it easier to identify patterns or anomalies.
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06:36
Scatterplots & Intro to Correlation

Correlation

Correlation refers to a statistical measure that describes the extent to which two variables change together. A positive correlation indicates that as one variable increases, the other also tends to increase, while a negative correlation indicates the opposite. Without a scatterplot, one might misinterpret the relationship between time and height, potentially overlooking important trends or suggesting a false correlation.
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05:43
Correlation Coefficient

Outliers

Outliers are data points that differ significantly from other observations in a dataset. They can skew results and lead to incorrect conclusions if not properly identified and analyzed. In the soccer ball experiment, failing to use a scatterplot could result in overlooking outliers that may indicate measurement errors or unique events, which could mislead the analysis of the ball's motion.
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04:48
Comparing Mean vs. Median
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Domanda del libro di testo

Time and Motion In a physics experiment at Doane College, a soccer ball was thrown upward from the bed of a moving truck. The table below lists the time (sec) that has lapsed from the throw and the corresponding height (m) of the soccer ball.

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a. Find the value of the linear correlation coefficient r.

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Exercises 1–10 are based on the following sample data consisting of costs of dinner (dollars) and the amounts of tips (dollars) left by diners. The data were collected by students of the author.

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Scatterplot Construct a scatterplot and comment on the pattern of points.

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Least-Squares Property According to the least-squares property, the regression line minimizes the sum of the squares of the residuals. Refer to the jackpot/tickets data in Table 10-1 and use the regression equation y^ = -10.9 + 0.174x that was found in Examples 1 and 2 of this section.

a. Identify the nine residuals.

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Casino Size and Revenue Use the same paired data from the preceding exercise.

b. What is the best predicted amount of revenue for a casino with a size of 200 thousand square feet? Is it likely that the best predicted amount of revenue will be accurate?



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Domanda del libro di testo

Time and Motion In a physics experiment at Doane College, a soccer ball was thrown upward from the bed of a moving truck. The table below lists the time (sec) that has lapsed from the throw and the corresponding height (m) of the soccer ball.

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b. Based on the result from part (a), what do you conclude about a linear correlation between time and height?

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Domanda del libro di testo

Notation The author conducted an experiment in which the height of each student was measured in centimeters and those heights were matched with the same students’ scores on the first statistics test.

a. For this sample of paired data, what does r represent, and what does represent?

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