Correlation Coefficient Quiz
This Correlation Coefficient Quiz assesses understanding of linear relationships and determination coefficients through practical data analysis. It evaluates skills in scatter plot creation, outlier identification, and correlation calculation, essential for statistical proficiency.
- 1.
A hi-fi store kept track of the number of advertisements it placed in local newspapers and the number of stereo systemsit sold each week.Week 1 2 3 4 5 6 7 8Advertisements, x 6 5 3 2 1 4 3 2Stereos Sold, y 20 15 12 8 6 7 9 7i. What is the correlation coefficient for the set of data?ii. What does this correlation coefficient suggest about the effectiveness of the advertisements?
- 2.
A manufacturer of flexible seals for industrial equipment tests samples of its seals at a variety of temperatures andcollects the following data.Temperature (ºC) 16; 5; 9; 12; 7; 10Seal Failures 3; 12; 8; 6; 4; 7a) Construct a scatter plot for these data.b) Identify any outlier(s) and explain your choice(s).c) Calculate the correlation coefficient for this data.
- 3.
A car safety association conducted tests to measure the stopping distances of a new model of car and collected thefollowing measurements.Speed (km/h) 30; 40; 50; 60; 70; 80; 90; 100Stopping Distance (m) 19.2; 22.2; 24.8; 27.1; 29.5; 31.6; 33.2; 35.0a) Construct a scatter plot for these data.b) Identify any outlier(s) and explain your choice(s).c) Calculate the correlation coefficient for this data.
- 4.
The coefficient of determination, r, indicates
- A.
The linear relationship between two variables
- B.
The slope of the line of best fit
- C.
How closely the data fit a defined curve
- D.
The sum of the residuals from each data point
Correct Answer
A. The linear relationship between two variablesExplanation
The coefficient of determination, r, indicates the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where a value of 1 indicates a perfect positive linear relationship, 0 indicates no linear relationship, and -1 indicates a perfect negative linear relationship. It is a measure of how well the data points fit a straight line, with higher values indicating a stronger linear relationship. Therefore, the correct answer is "the linear relationship between two variables."Rate this question:
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- 5.
Which of the following statements is false?
- A.
The coefficient of determination can have values from –1 to 1.
- B.
The coefficient of determination can be applied to any curve.
- C.
The coefficient of determination can be applied to any straight line.
- D.
The coefficient of determination is the variation in y explained by variation in x, divided by the total variation in y.
- E.
The magnitude of the correlation coefficient determines the strength of the linear relationship
- F.
The sign of the correlation coefficient determines whether the relationship is positive or negative
Correct Answer
B. The coefficient of determination can be applied to any curve.Explanation
The coefficient of determination, also known as R-squared, measures the proportion of the variation in the dependent variable (y) that can be explained by the independent variable (x). It ranges from 0 to 1, where 0 indicates no relationship and 1 indicates a perfect relationship. The coefficient of determination can only be applied to linear relationships, not curves. Therefore, the statement "The coefficient of determination can be applied to any curve" is false.Rate this question:
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Current Version
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Mar 20, 2023Quiz Edited by
ProProfs Editorial Team -
Aug 17, 2014Quiz Created by
Stickrathbrent