Questions and Answers
Does the dependent variable increase or decrease as the independent variable increases when two variables have a positive linear correlation?
What is the range of values for the correlation coefficient?
-1 to 1
Which value of r indicates a stronger correlation: r = 0.807 or r = -0.856? Explain your reasoning.
r = -0.856
What does r represent and what does p represent?
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What does it mean to say 'correlation does not imply causation'?
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What can you determine about the scatter plot of a paired data set if there is no linear correlation?
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Identify the explanatory variable and the response variable: A golfer wants to determine if the type of equipment used every year can be used to predict the amount of improvement in his game.
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What does Σx represent in the correlation coefficient calculation?
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In the context of the correlation coefficient, how do you find the product of x and y values?
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What is the process for performing a Linear Regression T-test in statistical calculations?
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What is the formula for calculating the critical values in a Linear Regression T-test?
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Is the slope of the regression line positive or negative when two variables have a positive linear correlation?
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What can be said about prediction values in relation to the original data?
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Match the following terms related to slope and y-intercept.
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What does the variable 'm' represent?
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Study Notes
Correlation Basics
- Positive linear correlation indicates that as the independent variable increases, the dependent variable also increases.
- The correlation coefficient (r) ranges from -1 to 1, with |r| closer to 1 indicating a stronger correlation.
- A stronger correlation is represented by r = -0.856 compared to r = 0.807 due to the absolute value comparison.
Correlation Coefficients
- "r" denotes the sample correlation coefficient, while "p" signifies the population correlation coefficient.
- Correlation does not imply causation; correlation alone cannot establish a cause-and-effect relationship between two variables.
Scatter Plots
- When a scatter plot displays no discernible pattern, it indicates no linear correlation between the pairs of variables.
Variables in Research
- In the context of golf improvement, the explanatory variable is the type of equipment used, and the response variable is the amount of improvement in the golfer's game.
Calculating Correlation Coefficient
- To find the correlation coefficient, calculate:
- Σx: Sum of x values
- Σy: Sum of y values
- Σxy: Sum of product of x and y
- Σx²: Sum of squared x values
- Σy²: Sum of squared y values
- "n" represents the number of data pairs.
Using Statistical Software
- For Linear Regression calculations:
- Input x-values in list 1 and y-values in list 2.
- Access the CALC menu to choose LinReg(ax + b) for regression calculations.
Linear Regression T-Test Process
- For hypothesis testing with a Linear Regression T-test:
- Input data into lists, then navigate to the TESTS menu.
- Select LinReg T-Test, choose the appropriate test symbol (not equal), and calculate.
Understanding Slope and Intercept
- In a positive correlation, the slope of the regression line is positive, indicating that as the independent variable increases, the dependent variable also tends to increase.
- Meaningful predictions for y based on x can only be made for x-values within or close to the range of the original data.
Key Terms
- Slope (m) represents the rate of change in y for each unit change in x.
- y-intercept (b) is the value of y when x equals zero.
- y values corresponding to data points and those corresponding to regression line points are denoted as yi and ŷi, respectively.
Studying That Suits You
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Test your knowledge of key concepts from Statistics chapters 9.1 and 9.2 with these flashcards. Each card focuses on essential terms and definitions related to correlation and variables. Perfect for review before exams or to reinforce your understanding.
