Math Problem Statement
The data below represent the number of days absent, x, and the final grade, y, for a sample of college students at a large university. Complete parts (a) through (e) below. No. of absences, x 0 1 2 3 4 5 6 7 8 9
Final grade, y 89.3 86.5 83.5 81.1 78.1 73.8 64.5 68.8 65.9 63.1 Question content area bottom Part 1 (a) Find the least-squares regression line treating the number of absences, x, as the explanatory variable and the final grade, y, as the response variable. ModifyingAbove y with caretequals enter your response herexplusleft parenthesis nothing right parenthesis (Round to three decimal places as needed.)
Solution
The least-squares regression line, treating the number of absences as the explanatory variable and the final grade as the response variable, is given by:
Where is the predicted final grade, and is the number of absences.
Do you need any further details or have any questions?
Here are five related questions:
- How can you interpret the slope of the regression line?
- What does the intercept represent in this context?
- How would you predict the grade for a student with 5 absences using this model?
- What is the significance of the value in this regression analysis?
- How can outliers affect the least-squares regression line?
Tip: Always check the residuals to assess how well your regression model fits the data!
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Math Problem Analysis
Mathematical Concepts
Statistics
Linear Regression
Correlation
Formulas
y = b0 + b1x (Least-squares regression line)
Slope formula: b1 = Σ[(x - mean_x)(y - mean_y)] / Σ(x - mean_x)^2
Theorems
Least-Squares Method
Linearity in Regression
Suitable Grade Level
College Level