Math Problem Statement
Solution
To solve the given problem and compute the least-squares regression line for predicting from , we use the formula for the regression line:
Step 1: Compute the slope ()
The formula for the slope is:
Where:
- (correlation coefficient),
- (standard deviation of ),
- (standard deviation of ).
Substituting the values:
Step 2: Compute the y-intercept ()
The formula for the y-intercept is:
Where:
- (mean of ),
- (mean of ),
- (slope).
Substituting the values:
Final Regression Line Equation:
Would you like further details or clarification?
Related Questions:
- How does the correlation coefficient influence the slope of the regression line?
- What is the significance of the standard deviations and in this context?
- How do you interpret the y-intercept in the context of this regression?
- Why is rounding to four decimal places important in regression analysis?
- Can the regression line be used for predictions outside the observed range of ? Why or why not?
Tip:
Always double-check the computation of and , as even small rounding errors can affect the regression line's accuracy.
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Math Problem Analysis
Mathematical Concepts
Statistics
Regression Analysis
Correlation
Formulas
b1 = r * (sy / sx)
b0 = ȳ - b1 * x̄
ŷ = b0 + b1 * x
Theorems
Least-Squares Regression
Suitable Grade Level
Grades 11-12, College Level
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