Math Problem Statement
Solution
Let's break down the information shown in the image step by step, related to a linear regression model connecting verbal scores and math scores.
Provided Regression Equation:
- Intercept (196.368): The predicted math score when the verbal score is 0.
- Slope (0.640): For each additional point in verbal score, the model predicts an increase of 0.640 points in the math score.
Questions:
e) Interpretation of the Slope
The question asks you to interpret the slope of the line, which is 0.640.
- Correct Choice (D): For each additional point in verbal score, the model predicts an increase of 0.640 points in the math score.
f) Prediction for a Verbal Score of 453
To predict the math score for a student with a verbal score of 453, substitute the verbal score into the equation: Rounded to one decimal place: 486.4.
g) Residual for a Perfect Verbal Score of 1600
To find the residual, we first calculate the predicted math score for a verbal score of 1600:
If a student scores a perfect math score of 1600, the residual is calculated as: Rounded to one decimal place: 379.6.
Summary:
- e): For each additional point in verbal score, the math score increases by 0.640 points.
- f): Predicted math score for a verbal score of 453 is 486.4.
- g): The residual for a student scoring 1600 on both verbal and math is 379.6.
Do you need further clarification on any of these steps? Here are 5 related questions to extend the topic:
- How does the R-squared value affect the accuracy of predictions in this model?
- What does the intercept of 196.368 represent in this context?
- How would the residual change if a student's actual math score was below the predicted value?
- What is the significance of the slope being positive in this regression model?
- How might this model differ if the relationship between verbal and math scores was non-linear?
Tip: When interpreting residuals, a positive residual means the actual value is higher than the predicted one, and a negative residual indicates the opposite.
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Slope Interpretation
Residual Calculation
Formulas
Linear regression equation: y = mx + b
Residual = Actual value - Predicted value
Theorems
Linear Regression Theorem
Suitable Grade Level
Grades 9-12