Grade 12 Math: Regression Analysis
This worksheet covers key concepts in regression analysis, including scatter plots, correlation, and linear regression equations, suitable for Grade 12 students.
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Regression Analysis Worksheet
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Read each question carefully and provide your best answer. Show all your work for calculations.
1. Which of the following describes a strong negative correlation?
As x increases, y tends to increase.
As x increases, y tends to decrease.
There is no clear relationship between x and y.
The data points form a perfect horizontal line.
2. What does the coefficient of determination (R-squared) represent?
The strength and direction of a linear relationship.
The proportion of the variance in the dependent variable that is predictable from the independent variable.
The average distance between the observed values and the regression line.
The slope of the regression line.
3. A plot is a graphical display used to investigate the relationship between two quantitative variables.
4. The variable is the variable that is being predicted or explained in a regression analysis.
5. A correlation coefficient of 0 indicates linear relationship between the variables.
6. Explain the difference between correlation and causation.
7. Analyze the scatter plot below and describe the relationship between the two variables (direction, strength, form).
8. A researcher collected data on the number of hours students studied for an exam (x) and their exam scores (y). The regression equation was found to be ŷ = 5 + 8x. Interpret the meaning of the slope and the y-intercept in this context.